Simplify: tan⁻¹( (cos x)/(1+sin x) ) = ? A. π/4 − x/2 B. π/4 + x/2 C. x/2 D. π/2 − x Answer: A) π/4 − x/2 Explanation: (cos x)/(1+sin x) = (sin(π/2−x))/(1+cos(π/2−x)) = tan(π/4 − x/2). So tan⁻¹ = π/4 − x/2, provided x ∈ (−π/2, π).

imo class 12 inverse trigonometric functions

Simplify: tan⁻¹( (cos x)/(1+sin x) ) = ?

VAVidaara Admin Asked 6d ago 0 views 0 answers

Simplify: tan⁻¹( (cos x)/(1+sin x) ) = ?

Answer: A) π/4 − x/2

Explanation: (cos x)/(1+sin x) = (sin(π/2−x))/(1+cos(π/2−x)) = tan(π/4 − x/2). So tan⁻¹ = π/4 − x/2, provided x ∈ (−π/2, π).