Question

Find the value of x for which (sin A + cosec A)² + (cos A + sec A)² = x + tan² A + cot² A.

Answer 1

(sin A + cosec A)² + (cos A + sec A)² = x + tan² A + cot² A

L.H.S. = sin² A + cosec² A + 2 sin A cosec A + cos² A + sec² A + 2 cos A sec A

= `(sin^2 A + cos^2 A) + (1 + cot^2 A) + 2 sin A xx 1/(sin A) + (1 + tan^2 A) + 2 cos A. 1/(cos A)`

= 1 + 1 + cot² A + 2 + 1 + tan² A + 2

= 7 + cot² A + tan² A

∴ x = 7