ConceptTrigonometric Identities

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#### Question

Prove the following identities:

`(i) cos4^4 A – cos^2 A = sin^4 A – sin^2 A`

`(ii) cot^4 A – 1 = cosec^4 A – 2cosec^2 A`

`(iii) sin^6 A + cos^6 A = 1 – 3sin^2 A cos^2 A.`

#### Solution

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#### Similar questions VIEW ALL

If secθ + tanθ = p, show that `(p^{2}-1)/(p^{2}+1)=\sin \theta`

Prove the following identities, where the angles involved are acute angles for which the expressions are defined

`(tantheta)/(1-cottheta) + (cottheta)/(1-tantheta) = 1+secthetacosectheta`

If acosθ – bsinθ = c, prove that asinθ + bcosθ = `\pm \sqrt{a^{2}+b^{2}-c^{2}`

Choose the correct option. Justify your choice.

`(1+tan^2A)/(1+cot^2A)`

A) sec^{2 }A

(B) −1

(C) cot^{2 }A

(D) tan^{2 }A

Choose the correct option. Justify your choice.

(1 + tan θ + sec θ) (1 + cot θ − cosec θ)

(A) 0

(B) 1

(C) 2

(D) −1

#### Reference Material

Solution for concept: Trigonometric Identities. For the course 8th-10th CBSE