# TRIGONOMETRIC IDENTITIES PROVING QUESTIONS

Trigonometric Identities Proving Questions

Here we are going to see, some example problems to show proving trigonometric identities.

## Trigonometric Identities Proving Questions - Questions

(1)  Prove the following identities.

(i) cot θ + tan θ = sec θ cosec

(ii) tan4 θ + tan2 θ = sec4 θ − sec2 θ

(2)  Prove the following identities.

(i)  (1 - tan2 θ) / (cot2 θ - 1)  =  tan2 θ

(ii) cos θ/(1 + sin θ)  =  sec θ + tan θ

(3)  Prove the following identities.

(i)  √[(1 + sin θ)/(1 - sin θ)]  =  sec θ + tan θ

(ii)  [√(1 + sin θ)/(1 - sin θ)] + [√(1 - sin θ)/(1 + sin θ)]  = 2 sec θ

(4)  Prove the following identities.

(i) secθ = tan6 θ + 3 tan2 θ sec2 θ + 1

(ii) (sin θ + sec θ)2 + (cos θ + cosec θ)2 = 1 + (sec θ + cosec θ)2

(5)  Prove the following identities.

(i) sec4θ (1 - sin4θ) - 2tan2θ  =  1       Solution

(ii)  (cot θ-cos θ)/(cot θ+cos θ) = (cosec θ-1)/(cosec θ+1)

Solution

(6)  Prove the following identities.

(i) [(sin A -  sin B)/(cos A + cos B)]  + [(cos A - cos B)/sin A + sin B)]  =  0     Solution

(ii)  [(sin3A + cos3A)/(sin A + cos A)] + [(sin3A - cos3A)/(sin A - cos A)]  =  2      Solution

(7)  (i) If sin θ + cos θ = 3 , then prove that tan θ + cot θ = 1.     Solution

(ii) If 3 sin θ − cos θ = 0, then show that tan 3θ = (3 tan θ - tan3θ)/(1 - 3tan2θ)    Solution

(8)  (i) If (cos α/cos β) = m and (cos α/ sin β) = n then prove that (m2 + n2) cos2β  =  n2          Solution

(ii)  If cotθ + tan θ = x and sec θ −cos θ = y , then prove that (x2y)2/3 - (xy2)2/3  =  1

(9)  (i) If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q(p2 −1) = 2p

(ii)  If sin θ (1+ sin2 θ) = cos2 θ, then prove that cos6 θ    −4 cos4 θ + 8 cos2 θ = 4

(10)  If cos θ / (1 + sin θ) = 1/a, then prove that (a2 - 1)/(a2 + 1) = sin θ After having gone through the stuff given above, we hope that the students would have understood, "Trigonometric Identities Proving Questions".

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