Prove the following identity (Sin x - cos x)^2 = 1 - sin(2x)  show work

Q: IT Evaluate the integral: (cos x + sinx cosx)dx

A:

Q: Evaluate the indefinite integral sin s cos sds

A: We have to solve

Q: Use the definitions of cosh x and sinh x to show that cosh2 x - sinh2 x = 1.

A:

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

A:

Q: 04) Prove that 1- Cos + x) = sin x, 2- (sin x +cos x) sec x = sec2 x %3D

A: We have to prove that following trigonometric identity.

Q: Prove that sin -1 x + cos -1  x = pie /2

A: We have to prove:

Q: Evaluate the integral ∫sin x/4 cosx/3dx.

A:

Q: Prove the identity. sin 2x = tanx 1+cos 2x

A: Explanation of the solution is given below....

Q: Prove sin 2x cot x (1 - cos 2x)

A:

Q: Q4: Prove that: (1- sin x)(1 + cscx) = cos x* cot x %3D

A: To Prove1−sinx1+cscx=cosx×cotx

Q: Prove the identity (sin x - cos x)2 = 1 - sin 2x

A:

Q: Prove the identity.   (cosh x + sinh x)n = cosh nx + sinh nx  (n is any real number)

A: The cosh x and sinh x are given by, LHS =

Q: Verify the following results  sin 4x = 8 cos3 x sin x − 4 cos x sin x

A: Given questions are two individual questions. So as per bartleby expert policy only one individual…

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

A:

Q: * Prove: sin x = cos COS 2- 2cos x

A:

Q: prove the followi Sin(zy) 1-Cos (zy) identity ng tancy)

A:

Q: Prove that sin 5x + sin 3x/4 sin x cos^3 x - 4 sin^3 x cos x = 2 cos x

A: Given: sin5x+sin3x4sinxcos3x-4sin3xcosx

Q: Prove the identity sinh 2x = 2 sinh x cosh x

A: Prove that: sinh 2x = 2 sinh x cosh x

Q: 46 a Show that cos x+ =-sinx. = -sinx. d" (cosx) = cosx + drn b Prove that

A:

Q: Prove (Start either from the LI 1- sin x 2. cosx COSx 1+ sin x

A: To prove : 1-sinxcosx=cosx1+sinx

Q: sin x + 10(csc x)² dx

A: To compute: ∫(sin x+10(csc x)2)dx

Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: Evaluate. de (sin(5x – 1)] cos(5æ – 1) 5 - sin(5æ – 1) 5 · cos(5æ – 1) • 5· cos(x)

A:

Q: 4. Prove that cos(sin¬1 x) = /1 – x².

A: cos(sin-1x)=1-x2⇒sin-1x=cos-1(1-x2)Let y=sin-1x                               (1) ⇒siny=x…

Q: Prove ONE of the follow sin x+ cos 2x-1 tan x %3D a) cos x-sin 2x

A:

Q: Prove the following identity. 1 - tan x 1 + tan x 1 - sin 2x cos 2x

A: Write tanx as sinx/cosx Multiply numerator and denominator by cosx to remove the fraction

Q: 2COTX Prove that Sin2x is an identity || csc2 x

A: we use the property of trigonometric function to shoe the result

Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: Prove the identity. s (xxy) sinx- sin (x-y) cosx= siny cos

A:

Q: Prove the below cos' x sin 3x + sin' x cos 3x 3 sin 4x 4 II

A: Simplification of trigonometry function

Q: Evaluate the integral: 3 X sin ³ COS 3 3 X col 3

A: Solved below.

Q: Prove the identity. + sin 3 cos x- cosx

A:

Q: Prove the identity. ex(1- sin'x) = So cosx | %3D

A: Prove the identity- Secx(1 - sin2x) = cosx. We know that : sin2x + cos2x = 1 Here i attached…

Q: IT Evaluate the integral: (cos x + sin x cosx)dx

A:

Q: Prove the following identity Sin^2xcos^5x=(sin^2x-2sin^4x+sin^6x)(cosx)

A:

Q: Prove the identity. cosh(x) + sinh(x) - e

A: To prove the given identity we uses basic expression for sinh(x) and cosh(x).

Q: Evaluate the definite integral 15 sin (3x) cos(3x) dx

A:

Q: 1 tan 0+ 1 sin 0 sin (90° – 0) tan 0 -

A:

Q: Evaluate integral 0 to pie sin 2 x cos 4 x dx

A: To Evaluate the integral given below:-I=∫0πsin2(x)cos4(x)dx

Q: Show that sin²(x) cos(x) = sec(x) – cos(x)

A: We need to show the following. So,         Manipulating right side=secx-cosx=1-cos2xcosx=sin2xcosx

Q: /2 Evaluate using Wallis' Formula: sin5 x cos6 x dx

A:

Q: Prove the identity. sec (-x) – sin (–x) tan (–x) = cos cosx

A:

Q: Evaluate the definite integral. • */10 cos 5x sin(sin 5x) dx

A:

Q: Verify the identity. sin 5x + sin 3x 2 cos x 4 sin x cos3 x - X – 4 sin x cos x 3.

A:

Q: Prove the identity. secx (1-sin'x) = cannot b cosx %3D

A:

Q: Evaluate the integral cos3 x + sin² x + 1 dx cos² x (sin2 x + 1)

A:

Q: Prove the identity. sin 2x cotx %3D 1- cos 2x

A:

Q: 5. Prove the following Identity: sin(2x) 1+ cos(2x) tan(x)

A: Use the following identities to prove  the given  identity. sin²x+cos²x=1 cos(2x)=cos²x-sin²x

Q: Evaluate integral 0 to pie sin 2 x cos 3 x dx

A: Explanation: Given that,  ∫0πsin2xcos3xdx   Formula Used: Trig. identity:1-sin2x=cos2xSum rule of…

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.