• tan xcos x = cotx %3D cScx • (1- sinx)[1+ sin(-x)] = •csc?x - cot2x =

Q: sin 2x Verify 1+ cos 2x = tan x.

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Q: [sin³ 4x cos 4xdx

A: We can find the answer as below.

Q: c) cos x tan x = sin x tanx %3D (Usx.SinzL (os x Sinc sinx cot x + = csc x - CSC X 1+cos x (e Sinzx…

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Q: 4 cos 4 cos dx () х3 sin3 4 - у4 - х dx

A: (1) using integration by substitution∫4 cos1x2x3 sin31x2 dxlet   sin1x2=udifferentiate both…

Q: cosx+sinx=cos(2x)  Prove that tanx=-1

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Q: (g) tan sec2 dx (c) sin“(3x) cos (3x) dx CoS'

A: Given: I1=∫sin43xcos33xdx, I2=∫tan4x2sec2x2dx

Q: Prove the identity. sinx 1+ cos.x 2 cscx 1+ cos.x sinx

A: Given, The identity  sinx1+cosx+1+cosxsinx=2cscx We have to prove the identity.

Q: 5. tan (x)dx 1 -dx cos² (x) sin () 6.

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Q: 6. cos x(csc x secx) secx) cotx

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Q: (A) Evaluate Sin (3x) Sin (3x) dx

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Q: [tan (x)sec (x)dx cot (x)csc°(x)dx sin (x)cos (x)dx

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Q: 1. tanx cscx-secx cot x sinx-cosx = sin x cos x 1 2. cscx-cotx cscx+cotx tan x 3. costx - sin*x = 1…

A: sinx-cosxtanx.cosecx-secx.cotx=sinx.cosxLHS=sinx-cosxtanx.cosecx-secx.cotxConvert all term in to sin…

Q: 7x cos()-7x [sin(-2x)sin(5x)sin(7x)] – lim 2x cos(x) lim x-0 5x?

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Q: sin 2x V2 – cos 2x dx

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Q: | (cos(3x) sin(x) – sin(3x) sin(x)) dæ

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Q: 75. sin x cos x dx 76. sin 2x sin (cos 2x) dx

A: as per the company guidelines, I can solve only one question.

Q: 4. sin2xcosx + sin x 1 xE[-27, Zn]

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Q: The simplified form of [csc(-x) +cos(-x)] - [10 sin² r sec²z]

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Q: 7. csc'x - cotx + tan'x CoSx - sin?xcosx

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Q: ∫sin5(6x)cos(6x)dx

A: ∫xn=xn+1n+1+C

Q: Verify the identity.

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Q: elin (sin x+ cos x) dx 1. S ecosx

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: 1-sin' x 3D sin.x 6. cosxcotx

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Q: VERIFY THE IDENTITY

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Q: cscxdx 5+ cos²x sin²x

A: Evaluate: I=∫csc2x5+cos2xsin2xdx We know that, cos xsin x=cot x Then, we have I=∫csc2x5+cot2xdx

Q: cos x sin x = csc 2x cos 3x sec 2x

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Q: 1. cos x 1 - sin x = sec x + tan x

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Q: sin4 x cos5 x dx

A: To solve: The integral ∫ sin4xcos5x dx Formula used: cos2x=1-sin2x Power rule of integration:…

Q: 1-sin x dx 1-cos x 2

A: Introduction :

Q: In(|tan(x) sin(x)|) = 2 In(|sin(x)]) + In(|sec(x)])

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Q: 1. sin x sin 2x + cos x cos 2x = COS X

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Q: 1-cos2.x sin 2.x : tanx

A: Given- 1-cos2xsin2x : tanx To Simplify- The above expression. Formula Used- cos2x=1-2sin2x and…

Q: S sin(1 – 2x)sin(2x + 3)dx

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Q: sin x (1- cosx) dx (1– cos² x)

A: To evaluate the integral: ∫sinx1-cosx1-cos2xdx Solution: Evaluating the given integral:…

Q: sin 4x cos 3x sin 2x tan 3z dx

A: (NOTE- Since it seems to be a typo mistake so, assuming that in the given integral all the variables…

Q: sin 7x dx 1 1 sin dx x cos² x 2 | (tan x + cot x) dx

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Q: 1+ cosx + sinx sinx 1+cos X 2sec x 2csc x 2csc 2x 2sec 2x

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Q: sin 3x cos“ 3xdx

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Q: sin(2x) dx cos(2x)+5 2x dx V3x +1 4 sec2(2x) dx ! 3(1-tan 2x)

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Q: cos x-sinxtanx=

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Q: sin(5x)+ sin(3x) tan(4x)= cos(3x)+ cos(5x)

A: We have to prove the identity

Q: dx 2 sin x - cOS X |tan+ 2 + V5| In 5 tan; + 2– V5 |tan+2-V5 + C + 2+ V5 2. + C In Option 1 O Option…

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Q: cos 2x-sin x 4. -(tan x +secx) %3D sin 2x - cos x

A: Given: prove that cos2x-sinxsin2x-cosx=-tanx+secx For verifying given expression, we solve left hand…

Q: sinx + sin 2 Evaluate | cosx A. -In cos x|– x+ C В. In'secx-x+ C C. -In|sec x|+ x+C D. In sec x|+x+C

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Q: 1+ cosx + sinx sinx 1+cos x 2sec x 2csc x 2csc 2x 2sec 2x X.

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Q: ) sin(2x) cos(5x) dx Scot (x) csc (x) dx

A: Given: 1.∫sin(2x)cos(5x)dx 2.∫cot3(x)csc4(x)dx

Q: Solve over the interval [0,2pi)

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Q: 3 sin³ (tan √x² + 3x²)] dx d [(x²+1) cotx dx 3- cos x csc x

A: To find the following derivatives.i ddx3 sin3tan x2+3x2ii ddxx2+1 cot x3-cos x csc x