Verify that each equation is an identity.  (Tan x / 1+ cos x) + (sin x / 1-cos x) = cot x + sec x csc x (1- sin θ / 1+sinθ) = sec^2θ - 2secθtanθ + tan^2θ

Q: Verify the identity by converting the left side into sines and cosines. (Simplify at each step.) 5…

A: Solve

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

A:

Q: Find the exact value sin[sin^-1(-4/5)-tan^-1(3/4)]

A: Use relation between sin-1 and tan-1   The expression is re written as,

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

A:

Q: Express sin 5x cos 3x as a sum of trigonometric functions.

A: Given           sin 5x cos 3x

Q: Verify the identity. sin x + sin x cotx= cSC X

A:

Q: Find sin x if cot x = -(√3)/2 and cos x

A:

Q: Verify the identity tan θ + cot θ = sec θ csc θ.

A: We have to verify tanθ+cotθ=secθ cscθ We know that tanθ=sinθcosθ and cotθ=cosθsinθ…

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

A:

Q: Verify the identity: (cos 4x - cos 2x)/(sin 2x - sin 4x) = tan 3x

A:

Q: Prove the identity. secx- cosx sinx tanx

A:

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

A: To prove the identity

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

A:

Q: Prove the equation Sin^2xcos^3x=(sin^2x-sin^4x)(cosx)

A:

Q: If tan x = 3, cos x > 0, , then - sin 2x cos 2x tan 2x %3D

A:

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: cot2 2x + cos2 2x + sin2 2x = csc2 2x

A: The given identity is ot2 2x + cos2 2x + sin2 2x = csc2 2x

Q: Verify that the equation is an identity. cos 2x = COS X - Sin x tan x CoS X To verify the identity,…

A: Using trigonometric formula, we verify

Q: Find the value of cos(4x) if = 4. 3 1-cos(x)-sin(x)

A: trigonometry

Q: Verify the Identity: tan sin = sec-cos

A: We verify this identity using relations between different trigonometric ratios & also using…

Q: 1-cosx sinx

A: Using Trigonometry property,

Q: verify the identity: tanx + secx = sinx + 1                            cosx

A: Given,

Q: Verify the identity -1 sin'0+2cose-1 1 sin 0+3cos0-3 1-sece

A:

Q: If x= ln (sec θ +tan θ) , show that sec θ = cosh x .

A: It is given that  x= ln (sec θ +tan θ)

Q: 10) Verify the identity sin0+cos0 sin0-cose %3D = sec0csc0 cose sino

A:

Q: verify that (sin(x)-cos(x))^2=1-sin(2x)

A:

Q: Complete the proof of the identity by choosing the Rule that justifies each step. cotx (1+ tan'x) -…

A:

Q: Verify the identity. cos 7x- cos 9x tan 8x sin 7x- sin 9x Statomont

A:

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: prove that: sin7x.cos3x-cos7x.sin3x/tan2x=cos4x+1

A:

Q: Verify Cot x+ 1 = CSCx (Cosx + sin x)

A: Right-hand side: CSCx (Cosx + sin x)=CSCxCosx+CSCxsinx---(1) We know that CSCx=1/sinx and…

Q: Verify the identity. (Simplify at each step.) cos³ x sin³ x = (sin³ x sin x)cos x cos³ x sin³ x =…

A: Given cos3x sin3x=sin3x-sin5xcosx

Q: Verify that the equation is an identity. sin x- cosx 1-2 sin x cosx Show that sinx+ cosx 1- 2 cos?x…

A:

Q: Prove that = tan 0 + cot 0 (cosec 0-sin 6)(sec 0-cos 0)

A:

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

A:

Q: Verify identity cos2 x - sin2 x = 1 - 2 sin2 x.

A: The given trigonometric equation (identity) is: cos2x-sin2x=1-2sin2 x To verify this, take the left…

Q: Verify the identity: tan2 2x + sin2 2x + cos2 2x = sec2 2x

A:

Q: Verify the identity. (Simplify at each step.) sin5/2 x cos x – sin9/2 x cos x = cos³ x/ sin5 x…

A: sin2X+cos2X=1 this is formula cos2X=1-sin2X

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. (Simplify at each step.) 5 sin2 x − 5 sin4 x = 5 cos2 x − 5 cos4 x   5 sin2 x…

A: Given identity is,5 sin2 x − 5 sin4 x = 5 cos2 x − 5 cos4 xConsider,5 sin2 x − 5 sin4 xTake out 5…

Q: Verify the identity 2 tan α/2 = (sin2 α + 1 - cos2 α)/sin α(1 + cos α)

A: Verify the identity 2 tan α/2 = (sin2 α + 1 - cos2 α)/sin α(1 + cos α)

Q: Prove the identity Sinx/1-cosx=secx+1/tanx

A:

Q: Prove the identity  cotx (1-cos2x)=sin2x

A:

Q: Verify the identity: (sin 2x + sin 6x)/(sin 2x - sin 6x) = -tan 4x cot 2x

A: We have to verify the identity: sin 2x+sin 6xsin 2x-sin 6x=-tan 4x cot 2x We know the sum and…

Q: Verify that 2tan (x/2)= (sin2x+1-cos2)/(sin x(1+cos x)

A: Consider the given condition that,2tan (x/2) = (sin2x+1–cos2x)/(sin x(1+cos x)) … (1)Consider the…

Q: evaluate sec(sin-1(3))

A: Given: