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#### Question

If sinθ + cosθ = p and secθ + cosecθ = q, show that q(p^{2} – 1) = 2p

#### Solution

#### Similar questions VIEW ALL

Prove the following trigonometric identities:

(i) (1 – sin^{2}θ) sec^{2}θ = 1

(ii) cos^{2}θ (1 + tan^{2}θ) = 1

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

Prove the following identities:

`( i)sin^{2}A/cos^{2}A+\cos^{2}A/sin^{2}A=\frac{1}{sin^{2}Acos^{2}A)-2`

`(ii)\frac{cosA}{1tanA}+\sin^{2}A/(sinAcosA)=\sin A\text{}+\cos A`

`( iii)((1+sin\theta )^{2}+(1sin\theta)^{2})/cos^{2}\theta =2( \frac{1+sin^{2}\theta}{1-sin^{2}\theta } )`

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

`(cosec θ – cot θ)^2 = (1-cos theta)/(1 + cos theta)`

Prove that ` \frac{\sin \theta -\cos \theta +1}{\sin\theta +\cos \theta -1}=\frac{1}{\sec \theta -\tan \theta }` using the identity sec^{2} θ = 1 + tan^{2} θ.