Question

Verify the following with the help of identities.

(i) tanθ/(1 - cotθ) + cotθ/(1 - tanθ) = 1 + sec θ cosecθ

(ii) (sin A + cosec A)² + (cos A + sec A)² = 7 + tan²A + cot²A

Answer 1

(i) LHS = tanθ/(1 - cotθ) + cotθ/(1 - tanθ)

= 1 + sec θ cosecθ

= R.H.S.

(ii) LHS = (sin A + cosec A)² + (cos A + sec A)² 

= 5 + sec² A + cosec² A

= 5 + (1 + tan² A) + (1 + cot² A)

= 7 + tan² A + cot² A

R.H.S.