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We can expand our integrand into a series using the binomial formula $$(ab)^m=\sum_{k=0}^m{m\choose k}a^{mk}About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy &Safety How works Test new features Press Copyright Contact us Creators

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What is sec^2x-tan^2x-Recall the double angle formula cos(2x) = cos^2(x) – sin^2(x) We also know the trig identity sin^2(x) cos^2(x) = 1, so combining these we get the equation cos(2x) = 2cos^2(x) 1 Now we can rearrange this to give cos^2(x) = (1cos(2x))/2 So we have an equation that gives cos^2(x) in a nicer form which we can easily integrate using theA formula can often be simplified, as wasAbout Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy &

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Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with stepbystep explanations, just like a math tutorDefine mathfR \to R/math by mathf(x)=tan(2x)2x/math Then mathf'(x)=2sec(2x)2>=0/math on math(\pi/2,\pi/2)/math which means mathf/math is$$\int \sec^2x \tan^2x dx= \frac{tan^2x}{3} \frac{c}{3}$$ Note that as $c$ is an real number we could replace $\frac{c}{3}$ with $c_2$ to write the answer more neatly as $$\int \sec^2x \tan^2x dx= \frac{tan^2x}{3} c_2$$

Keep breaking it down until you find something you can work with Let u=sec^2 and v=tan^2 and if that's still too much at this stage Let a=sec b=sec c=tan d=tan Differentiate a and b, use the product rule to find u;For each of the three trigonometric substitutions above we will verify that we can ignore the absolute value in each case when encountering a radical 🔗 For x = asinθ, x = a sin ⁡ θ, the expression √a2 −x2 a 2 − x 2 becomes √a2−x2 = √a2−a2sin2θ= √a2(1−sin2θ)= a√cos2θ= acosθ = acosθ a 2 − x 2 = a 2 − a 2Ex 74, 9 sec 2 tan 2 4 Let tan = Diff both sides wrt x sec 2 = = sec 2 Integrating the function sec 2 tan 2 4 Putting value of tan = and = sec 2 = sec 2 t

Starts from RHS to LHSFree math lessons and math homework help from basic math to algebra, geometry and beyond Students, teachers, parents, and everyone can find solutions to their math problems instantlyWell, if we divide (cos(x))2 on both sides;

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Given Data The differential equation is shown as, {eq}\frac{{{d^2}y}}{{d{x^2}}} 4y = 4\sec 2x\tan 2x {/eq} To obtain the particular solution use Wronskian differential equation as,Sec^4xtan^4x = (sec^2xtan^2x) (sec^2xtan^2x) = (1tan^2xtan2^x) (1tan^2xtan^2x) = (1) (12tan^2x) = (12tan^2x) Your question should be modfied as;Answer to Solve the trigonometric equation on the interval \\parenthesis 0,2\\pi \\parenthesis \\tan(2x) 1 = \\sec(2x) By signing up, you'll get

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Evaluate the following integral using logarithmic formula Show transcribed image text Expert Answer Transcribed Image Text from this Question 1 S sec(2x) tan(2x) dx 2 3 tan(2x) ( 2x5 – 4x* x2 4x2 5x 15 )dx 2 s 2x2 3 3 s (x 1)dx ( 3x 2)2 Get more help from Chegg Solve it with our calculus problem solver and{eq}A \ 1\sin^3x \\ B \ \sec^4x2\sec^2x\tan^2x\tan^4x {/eq} Simplification Simplification is a method of deducing a basic form using factor, multiplication and division rules from the givencos(ax)cos(bx) = 1 2cos((a − b)x) 1 2cos((a b)x) These formulas may be derived from the sumofangle formulas for sine and cosine Example 726 Evaluating ∫ sin(ax)cos(bx)dx Evaluate ∫sin(5x)cos(3x)dx Solution Apply the identity sin(5x)cos(3x) = 1 2sin(2x) 1 2sin(8x)

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Differentiate c and d, use the product rule to find v Then just use the product rule on u and v 0Separate fractions Rewrite tan(x) tan ( x) in terms of sines and cosines Multiply by the reciprocal of the fraction to divide by sin(x) cos(x) sin ( x) cos ( x) Convert from cos(x) sin(x) cos ( x) sin ( x) to cot(x) cot ( x) Divide sec2(x) sec 2 ( x) by 1 1 Rewrite sec(x) sec ( x) in terms of sines and cosinesTrigonometry Graph y=sec (2x) y = sec(2x) y = sec ( 2 x) Find the asymptotes Tap for more steps For any y = sec ( x) y = sec ( x), vertical asymptotes occur at x = π 2 n π x = π 2 n π, where n n is an integer Use the basic period for y = s e c ( x) y = s e c ( x), ( − π 2, 3 π 2) ( π 2, 3 π 2), to find the vertical

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DSinghvi 535 3 3 silver badges 16 16 bronze badges Add a comment 0 we have to show that sec(x)2 tan(x)2 − (1 − sin(x)4)sec(x)4 = 0, the left hand side is equivalent to sin ( x)4 − 1 cos ( x)4 sin ( x)2 1 cos ( x)2 = ( sin ( x)2 − 1) ( sin ( x)2 1) ( sin ( x)2 1) cos ( x)2 cos ( x)4Cos^2xsin^2x 2cos^2x1 12sin^2x sin2x= 2sinxcosxStart studying Trigonometric Identities for Calculus 2 Learn vocabulary, terms, and more with flashcards, games, and other study tools

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$\begingroup$ What I get from this is that in contrast to the (usual?) direction/order where one starts with hypotheses and sees what can be derived, here one first has a conclusion in mind to aim for (the equation, the $\int f'g = fg \int fg'$ formula, etc) that feels in some sense that it 'ought' to hold and then imposes conditions toBut that's just the binomial formula ((tan ⁡ (x)) 2 1) 2 = (sec ⁡ (x)) 4 but (tan ⁡ (x)) 2 1 = (sin ⁡ (x)) 2 (cos ⁡ (x)) 2 (cos ⁡ (x)) 2 and the numerator is known to be 1 for all x given the definition fo sin and cos and the Pythagorean theorem, so we have (1 (cos ⁡ (x)) 2) 2 = (sec ⁡ (x)) 4Get stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!

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Learn how to solve trigonometric integrals problems step by step online Solve the trigonometric integral int(sec(2x)tan(2x))dx We can solve the integral \int\sec\left(2x\right)\tan\left(2x\right)dx by applying integration by substitution method (also called USubstitution) First, we must identify a section within the integral with a new variable (let's call it u), which when substitutedFree PreAlgebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators stepbystepSec^4xtan^4x Approved by eNotes

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Sec2(2x) sec 2 ( 2 x) Because the two sides have been shown to be equivalent, the equation is an identity tan2(2x)sin2(2x) cos2(2x) = sec2 (2x) tan 2 (Proving $(\sec^2x\tan^2x)(\csc^2x\cot^2x)=12\sec^2x\csc^2x$ and $\frac{\cos x}{1\tan x}\frac{\sin x}{1\cot x} = \sin x \cos x $ 0 How to find the least value of $\cot x \frac{\csc^2x\cot ^4x}{\csc^2x\cot x}\tan x \frac{\sec^2x\tan^4x}{\sec^2x\tan x}$?1Solve tan^2x tan x – 1 = 0 for the principal value (s) to two decimal places 6Prove that tan y cos^2 y sin^2y/sin y = cos y sin u0004y 10Prove that 1tanθ/1tanθ = sec^2θ2tanθ/1tan^2θ 17Prove that sin^2wcos^2w/tan You can view more similar questions or ask a new question

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Yes, sec 2 x−1=tan 2 x is an identity sec 2 −1=tan 2 x Let us derive the equation We know the identity sin 2 (x)cos 2 (x)=1 ——(i) Dividing throughout the equation by cos 2 (x) We get sin 2 (x)/cos 2 (x) cos 2 (x)/cos 2 (x) = 1/cos 2 (x) We know that sin 2 (x)/cos 2 (x)= tan 2 (x), and cos 2 (x)/cos 2 (x) = 1 So the equation (i) after substituting becomesA follow up proof to accompany sin^2 cos^2 =1 Another identity that is used quite a bit, especially in calculus involving trigonometric functionsYour approach is a little long How about $\sec^4x=(\sec^2x)(\sec^2x)=\sec^2x(\tan^2x1)=\sec^2x\tan^2x\sec^2x$ Now you can integrate?

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Free derivative calculator differentiate functions with all the steps Type in any function derivative to get the solution, steps and graphand we find sec2x −tan2x = 1 cos2x − sin2x cos2x sec2x −tan2x = 1 −sin2x cos2x sec2x −tan2x = cos2x cos2x sec2x −tan2x = 1Integral of sec^2x \square!

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Solve for x tan (2x)=1 tan (2x) = 1 tan ( 2 x) = 1 Take the inverse tangent of both sides of the equation to extract x x from inside the tangent 2x = arctan(1) 2 x = arctan ( 1) The exact value of arctan(1) arctan ( 1) is π 4 π 4 2x = π 4 2 x = π 4 Divide each term by 2Safety How works Test new features Press Copyright Contact us CreatorsWe seek to solve d 2 y/dx 2 4y = 4 sec 2x tan 2x (1) subject to the initial conditions y(0) = 3 y'(0) = −4 (2) (a) Find the solution to the homogeneous equation with the nonhomogeneous boundary conditions (yh)

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Free trigonometric identities list trigonometric identities by request stepbystepChain Rule To find the derivative of this function, first rewrite it as f(x) = (secx)2(tanx)2 f ( x) = ( sec ⁡ x) 2 ( tan ⁡ x) 2 We will use the chain rule on each term Recall thatIntroduction to Tan double angle formula let's look at trigonometric formulae also called as the double angle formulae having double angles Derive Double Angle Formulae for Tan 2 Theta \(Tan 2x =\frac{2tan x}{1tan^{2}x} \) let's recall the addition formula

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The wrong formula was used for the Disk Method, it should be the integral from 1 to 2 of \pi(\sec^2(x1)\ln^2 x) (The Shell Method was also incorrectly set up, that integral represents volume The wrong formula was used for the Disk Method, it should be the integral from 1 to 2 of π ( sec 2 ( x − 1 ) − ln 2 x )2 x I started this by making sec 1/cos and using the double angle identity for that and it didn't work at all in any way ever Not sure why I can't do that, but something was wrong Anyways I looked at the solutions manual and they magic out 1 tan ⁡ x tan ⁡ 2 x = 1 tanWe get (tan(x))2 1 = (sec(x))2 1 = (sec(x))2 (tan(x))2 Now, we will see if 1 = (sec(x))2 (tan(x))2and 1 = (sec(x))2 (tan(x))2 can

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Find all solutions of sec^2xtan^2x=3 in the interval 0,2piSince tan^2 = sec^2 1 you getsec^2 sec^21 = 3 2sec^2= 4 sec^2 = 2 sec(x) = sqrt(2) cos(x) = 1/sqrt(2)Take the cos^1(x) to get x = cos^1(1/sqrt(2)) or x = cos^1(1/sqrt(2))x =

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