Prove the identity 1/Cos X - 1/Sec X = Tan X * Sin X

Q: Verify the identity: 1- sin(2x) 1- tan x cos(2x) 1+ tan x

A: LHS: 1-sin(2x)cos(2x)=cos2x+sin2x-2sin(x)cos(x)cos2x-sin2x ( as…

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: Verify the identity     sec x + tan x = cos x /(1 − sin x) .

A: Our Aim is to prove the trigonometric identity given below:- sec x + tan x = cos x /(1 − sin x)…

Q: Verify the identity: (cos 3x - cos x)/(sin 3x + sin x) = -tan x.

A:

Q: prove the identity cos^3x sin^3x =(sin^3x-sin^5x)cosx

A:

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

A: We have to prove:

Q: Verify the identity: (cos 3x - cos 5x)/(sin 3x + sin 5x) = tan x.

A:

Q: Prove the identity sec x - cos x = sinxtanx

A: To prove the identity

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

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

Q: Verify the identity : (1 - cos 2x)/sin 2x = tan x

A: Given that:   To use the angle formulae: cos 2x = cos 2 x - sin 2 x sin 2x = 2 sin x . cos x sin 2 x…

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

A:

Q: Verify the identity -tan x  = cos 3 x - cos x / sin 3 x + sin x

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Q: Prove the identity. cos(3x) − cos^3 x = − cos x sin^2 x − sin x sin(2x)

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Q: Prove the identity. sin x+ 2. = cotx sin (n-x)

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

A: we have to verify the identity

Q: Verify the identity sec-1 x = cos-1(1/x), for x ≠ 0.

A: According to the question, we have to verify the identity sec-1x=cos-11x. As the above function is…

Q: Verify the identity: tan(-x)cos x = -sin x

A: To verify:      tan(-x)cos x = -sin x We will start from LHS and will try to get RHS.

Q: Prove the identity. sin 2x- sin 6x - tan 2x cos 2x+ cos 6x

A: The objective is to prove The Identity.

Q: Prove the identity  Cos x/1+sin x + Cos x/ 1-sinx = 2sec x

A:

Q: Prove the identity. secx- sin x tanx= cosx

A: Given,          secx-sinxtanx=cosx

Q: 9. Establish the identity: tan2 +1 sec x 1 = sec x LHS

A: Establish the identity

Q: Establish the identity. (5-) - sin cos 0 %3D

A: Given,          sinπ2-θ=cosθWe know that,           sinA-B=sinAcosB-cosAsinB

Q: Prove sin (90◦+x) + sin (90◦−x) = 2 cosx

A:

Q: Verify. the. identity cos(x)sin(x)tan(x)=csc(x)-cot(x)-cos^2(x)

A: To verify: cos(x).sin(x).tan(x)=cosec(x)-cot(x)-cos2(x)

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

A:

Q: Verify the identity: sec x - 1 = sec x 1- cos x

A: Now , we will verify the identity.  We know,  1/cosx = secx .

Q: Verify the identity: sin (3π/2 - x) = -cos x

A: To prove  sin (3π/2 - x) = -cos x

Q: Verify the identity. tan (-x) cos X - sin x

A:

Q: 3. Prove the identity tan * COS v t CSC x Sinx=2sinx

A: Prove the identity

Q: Verify the identity: [sin 2x + (sin 3x + sin x)]/[cos 2x + (cos 3x + cos x)] = tan 2x

A: Consider the identity, sin2x+sin3x+sinxcos2x+cos3x+cosx=tan2x To apply the trigonometric identity,…

Q: Verify the identity: cot(-x) sin x = -cos x

A: cot(-x)=-cot(x)cot(x)=cos(x)sin(x)

Q: Verify the identity : sin(x + π)/cos (x + 3π/2) = tan2 x - sec2 x

A:

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: Prove the identity. cos x- secx=-sinx tan x 2.

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

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Q: Verify the identity: cos x/(1 - sin x) + (1 - sin x)/cos x = 2 sec x

A: The given identity is cosx1-sinx+1-sinxcosx=2secx

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

A: sec(-x)-sin(-x)tan(-x)=sec(x)-(-sin(x))(-tan(x))=sec(x)-sin(x)tan(x)

Q: prove the identity sin^2xcos^2x+cos^(4)x=(1-sinx)(1+sinx)

A:

Q: Verify that (sin(x) – cos(x)) = 1- sin(2x)

A: sinx-cosx2=sin2x-2sinxcosx+cos2x     ∵a-b2=a2-2ab+b2=sin2x+cos2x-2sinxcosx=1-sin2x…

Q: verify the identity  1 + sec ^2 x/ 1 + tan ^2 x = 1+ cos^2x

A: Note that 1+tan^2x = sec^2x  1/sec2x= cos2x

Q: . Prove only 1 of the 2 identities given. sin x 1-cosx = 2 csc x 1-cos x sinx -) 1- sin? x – sin² y…

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Q: Prove the identity. cos (-x) 1- sin (-x) = secx- tanx

A:

Q: 1. Verify the expression cos(x) + sin x tan x = secx.

A: Given, cos x + sin x tan x = sec x

Q: Prove the identity. cos (-x) 1- sin(-x) secx- tanx

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Q: prove  cosx( 1- tan x)= cos x- sin x

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Q: Verify the identity. sin 3x 1 = 2 cos x- %3D sec x 2 - sin 2x

A: Given: Verify the identity sin3xsin2x=2cosx-12secx for verifying given identity we solve left hand…