12 (b) sec ( sin 13

Q: 2cos(2x)sin(2x)-sin(2x)=0

A:

Q: 1 -dx = /8-(2x+5)² o įsin- (2*) 2x+5 + c V8 2x+5 sin-1 + c 8, tan- ( V8 2x+5 + c o ţtan" (2*5 ) + c…

A:

Q: 1 -sin(2x)% = (D²-1 -1 sin(2x) 125 O ibs

A:

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: 5. y = tan- (a) 6. y = 4x sin (3x - 9) 7. y = sinh (4x – 1)

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Q: |5sin(4x + 5) sin(2x --) dx

A: We need to evaluate the given integral. We will use the formula  Cos(A+B)-Cos(A-B)=-2 SinA SinB

Q: gral. cos 7x cos 4x dx ㅇ응 cos 3x + 숲 cos 11x + C ㅇ sin 3x + sin 11x+C 1 sin 3x - sin 11x +C

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Q: 1 sec- x = cos

A: Given, sec-1x=cos-11x   Check it is True or False:

Q: 5) 3tan-1x + sin-x = 4

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Q: 9 sin5(x) cos³(x) dx

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Q: 2/2 2 sin³(x) dx

A: Here is the solution of the given problem.  To solve the problem we use the following formula:…

Q: sin(4x) cos(2x) dx = cos (2x) cos (6x)' sin (2x) cos (2x) сов (10х) 4. (2x) sin (10x)+ c sin +c 10…

A: Use formula 2sinAcosB=sin(A+B)+sin(A-B)

Q: 3 (4+sin-15x)° dx (8) V1-25x2

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Q: 4. y = tan¬1(3x) cos 1 4x 5. y =

A: To determine the derivative of given functions. Here we will use the following formulas-…

Q: √2 2 sin-¹(x)dx

A:

Q: 6. G) sec 4 tan .3. dx 3 (),

A: Consider the given integration ∫tan6x3sec4x3dx

Q: sin20 6. J 1-cos 0

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Q: 10x 19) y Sin'(5x') (ans.: JI-25 x' 20) y= Cot ) (ans.: 1+ x' 6x' 21) y=tan'V4x'- 2 (ans.: (4x'-1…

A: As per guidelines we can only solve first question or first three subparts of the question, I am…

Q: sin(2x) cos(2x) dx 1+ cos(4x)

A: The complex form of integral can be converted to simple integral using integration by substitution…

Q: [*(sin³r)√1 + cos ar dr x

A: We know that integration power rule is given as  Integration of xn is xn+1/n+1.   Here i attached…

Q: 21. cos x cos 2x + sin x sin 2x

A:

Q: 3 3 | sin sin x cos xdx 5

A: It is integration problem.

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: Evaluate the integrals

A: Given integral: ∫π6π2sin2x2sinxdx

Q: 5. 4 (secx-1)(sec² x+secx+1) Sª cos² 2x-2 cos 2x+1 -dx

A: Indefinite integral is the process through which one can determine the function which on…

Q: 13. sec*0 sin 8 de

A:

Q: 7/4 (sec² x – sin x)dx

A: 1. ∫sec2x dx=tanx 2. ∫sinx dx=-cosx 3.∫(u±v)dx=∫u dx±∫v dx 4. ∫abf(x) dx=F(b)-F(a), where ∫f(x)…

Q: tan20 21-25. Verify = sec?e – sec 0 cose + 1

A: To verify: That tan2θcosθ+1=sec2θ-secθ. Formula used: Trigonometry identity: tanθ=sin θcos θ…

Q: sin(-4x) cos 3x dx 1. 3

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Q: 1/sin ^2x + 1/cos^2x=1/sin^2x cos^2x

A: 1/sin ^2x + 1/cos^2x=1/sin^2x cos^2x

Q: cos 2x+1 sin 2.x 7. Prove that sin 2x 1-cos 2x

A: The trigonometric of an acute angle in a right triangle express the relationship between the angle…

Q: 7- I = [sec(2x) tan(2.x)dx cos(2x) 8- I = dx 4-sin (2x) csc (In(x)) 9. I: dx

A:

Q: Si cos°(3x)sin (3x) – cos (3x) sin°(3x) dx

A: First we common out cos7(3x) sin7(3x) and then apply the formula cos2(3x)-sin2(3x)=cos(6x)

Q: Establish the identity.

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Q: sin 0- cos 0 = V2

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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: cos^2x+sin^2x/cos^2x=

A:

Q: 1- cos 4x sec2 2x – 1 = 1+ cos 4x

A: Question is solved.

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

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Q: 2 sin 1 3 -1 cos tan 4

A:

Q: | cos(x) (8 + 4 sin²(x)) dx

A: Given Data: Integral Expression: ∫cosx8+4sin2xdx   Let, sinx=u Differentiate above equation.…

Q: 1- cos 4x 9. sec2 2x – 1 = 1+ cos 4x

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Q: 3. у %3D tan1(sinh 2x) Зсosh-1 (csc) 4. у %3 CSC

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Q: cosh(3i)is equal to O -cos3 O cosh 3 cos 3 O sin 3

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Q: sin(4 + 5x) cos (5x – 4)dx

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

A:

Q: Estimate sin 2.9. (Round your answer to one decimal place.) sin 2.9 =

A: This question is based on identifying radian and y term in given circle.