Compute / sin x •cos1º x dx.

Q: 4. Evaluate sin (x) cos°(x)dx

A: To evaluate the integral

Q: 1- Determine. 4. Cos 'x sinX dx

A: Given:                     ∫cos4(x) sin(x) dx     Solution:                    Integrating the given…

Q: Prove that  d/dx[cosx]=-sinx

A: We will use the definition of the derivative  Here f(x)=cos(x) So,

Q: (b) ſ sin³(x) -dr cos (1)

A: Let's solve given integration.

Q: Evaluate the integral ∫sin5 x/3 cos x/3 dx

A:

Q: 2. tan3x(sec3x – cos3x) dx

A:

Q: Verify sin (x +) = cos(n – x) %3D

A:

Q: Express the 10th term of ( x1 + x2)º in terms of sinusoidal functions (sin, cos).

A: The expression is x1+x220. As we have obtained…

Q: Evaluate sin (3x) cos (6x) dx Select one: cos(9r) A cos(3r) tC 18

A:

Q: Evaluate sin(x) 1+cos(x) -dx

A:

Q: Evaluate ∫sin2 x cos4 x dx.

A:

Q: Prove the identity. sin(x+y) sinx + cos(x+y) cosx = cosy

A:

Q: Evaluate: / [cos(x) – sin(x) ]dx

A:

Q: sin (3x+1)dx 4 cos (3x+1) C

A:

Q: Find sin 4.x cos 8x dx.

A:

Q: Verify the identity. cos x = sin x sin 2x + cos x cos 2x

A: we have to verify the identity

Q: Evaluate (2 cos x-sin x)² -dx sin x

A: We have to solve the above integrals

Q: sin x dx V2-cos² x

A: Given : ∫(sin x/√2 - cos2 x) dx     ....(1)   Let cos x = t   Differentiating both sides w.r.t. x -…

Q: Find the first and second derivatives of r = [3 cos 2t, 3 sin 2t , 4t].

A:

Q: Differentiate.  y =cos x /(1 - sin x)

A:

Q: dr de sin - r- cos + eª cos = 0

A:

Q: Verify the identity. sin(x + y) – sin (x - y) = 2cos.xsiny

A: To verify the identity, sinx+y-sinx-y=2cosxsiny

Q: Evaluate 2 sin² x cos³ x dx 0,

A: Given that: ∫0π2sin2x.cos3xdx

Q: Compute : exp(i sin(e-i))

A:

Q: ( sin (In 2x) - cos (in 2x))? +x dx 2x

A: Let's find.

Q: Prove the identity. cosx sin (x+y) – sinx cos (x+y)= siny

A: In question We have given two identities and we'll prove it, (i). Cos(π + x) = - Cosx  (ii). Cosx…

Q: 3 + cos 3x dx Evaluate sin 3x

A:

Q: Verify. esc (x) [I-cos(2x)] = 2 sin (x) SC

A:

Q: Evaluate the integral. ∫ Cos2 x Sin2x dx

A: Given :           ∫cos2x sin2x dx

Q: x is in the interval [0, 2t) * sin2x - cos2x = 0 COS

A: Given: sin2x-cos2x=0; x∈[0,2π) We know that cos2A-sin2A=cos2A…

Q: Q1 : limx¬1 x(1 – cos-)

A: To find the limit

Q: Differentiate the function. f(x) = 5 sin2(x) − 8 cos2(x)

A: Given:

Q: Calculate ∫9sin^4(x)cos^2(x)dx

A: Given: ∫ 9 sin4 x cos2 x dxFormula: cos2 x = 1-sin2 x…

Q: Integrate x3 cos(x4)

A:

Q: S cos3 x sin* x dx

A:

Q: determine the value of sin^2 x + cos^2 x for x =10 degrees

A: Given x= 10 degrees By trigonometric formula we know that , sin2(x)+cos2(x)=1 where x∈-∞,∞

Q: Evaluate sin z -dx /4 - coS I

A: Use the substitution method and first simplify the integration than integrate.

Q: 2. Evaluate x sin x cos xdx.

A:

Q: Evaluate: [e* 1+ sin 2x dx 1+ cos 2x

A: Topic:- Integration

Q: Evaluate sin integral (4x) cos(5x) dx

A:

Q: Evaluate cosx (2 + sin x)°dx

A:

Q: What is the value of d. (sin x3 dx cos x²)? COS

A:

Q: Evaluate: cos³x dx sinx I =

A: We know that : sin2x + cos2x =1. we know that integration of xn = xn+1/ n+1 We use all of  this to…

Q: Show that n/2 sin x dx sin x + coS X %3D 4

A:

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.