Use the fundamental identities to simplify the expressic 9 sec2 x(1 - sin2, n²x)

Q: (tan® – sin®)²+(1 – cos®)²= (1 – sec0)²

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Q: Use the addition formulas to derive the identities in Exercise

A: There are six trigonometric ratios those are sine, cosine, tangent, cosecant, secant and cotangent.…

Q: Prove the identity. secx- sinx tanx cosx

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

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

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Q: Verify the identity: sec(α + β) = sec α sec β/(1 - tan α tan β)

A: Given sec(α + β) =secα secβ1- tanα tanβ∵sec θ = 1cos θ ; tan θ = sin θcos θ⇒ from (1) , we get…

Q: 1-cos2x/1+sinx=sinx. Prove the identity

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Q: a) Buktikan, Prove that, (sin x + cosx)* = sin 2x + 2 sin 2x +1.

A: The given equation,sinx+cosx4=sin22x+2 sin2x+1

Q: Verify the identity. sin 3x = 3 sinx – 4sin'x %3D

A: We have to verify the identity: sin 3x=3 sin x-4 sin3 x Taking LHS, we get LHS=sin 3x=sin 2x+x We…

Q: Prove: sin (2 cosx) = 2x1-x

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Q: Prove the identity. cos²x 1+ sinx (1– sinx)? 1- sinx

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Q: Prove the identity  secx-sinx tanx=cosx

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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: prove that: tan(x/2)= (sinx/1+cosx

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Q: 3. Rewrite the expression tan (2x) sec² (2x) entirely in terms of tangent.

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Q: Prove the identity. 1+ sinx cosx =2 seex cosx 1+ sinx

A: We need to prove the following identity 1+sinxcosx+cosx1+sinx = 2secx

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

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Q: Prove the identity. cosx- cos 7x tan 3x %3D sinx+ sin 7x

A: Here we use basic formulas of trigonometric ratios to find addition and subtraction.

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

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Q: Verify: 1. (sinx – cosx)² – 1 = -sin2x %3D

A: We can verify the statement as below

Q: verify the identity

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Q: prove that sin⁴x - sin²3x+sinx-3 = 0 has no solution.

A: prove that sin⁴x - sin²3x+sinx-3 = 0 has no solution.

Q: [1] sin3x Asinx – Bsin³x, find A and B. -

A: Explanation of the answer is as follows

Q: prove the identity cosx + sinxtanx= secx

A: The given identity,cosx+sinx tanx=secx

Q: 3. Rewrite sec (tan-u+ cosv) (a, algebraic expression. as an

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Q: Prove the identity. 1+ cosx + sinx sinx =2 cscx 1+ cosx

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Q: Use the fundamental identities to fully simplify the expression : 1-sinx 1-sira +200s x 2-sinx None…

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

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Q: Use fundamental identities to simplify the expression  cosx-cosx sin^2 x

A: We have to simplify the expression.Expression is given below:

Q: verify the identity sin2x-sin2y=cos2y-cos2x

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

A: We have to prove that sin2θ+2cosθ-1sin2θ+3cosθ-3 = 11-secθ We will using the following property to…

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

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Q: Derive/Prove: sin 2x = 2 sin x cos x

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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: Verify the identity : 2 sin2x-1= 1- 2 cos2x

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Q: What is the greatest possible value for the product of 2-sinx and 3 + cos5x

A: (2-sin(x))(3 + cos(5x)) =6-3sin(x)+2cos(5x)-sin(x)cos(5x)

Q: Verify the identity by transforming the lefthand side into the right-hand side.

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

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

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

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Q: 3. Rewrite the expression tan (2x) sec²(2x) entirely in terms of tangent.

A: Given: tan52xsec22x Formula Used: sec2x+tan2x=1