Question

Simplify tan-1 (sin x + cos x/ sin x - cos x)

Answer 1

Answer:tan−1(cos(x)−sin(x)cos(x)+sin(x)),0<x<π

Answer 2

Answer:

Step-by-step explanation:

tanx - 1 (sinx + cosx / sinx - cosx) =

(sinx/cosx) - 1  × (sinx + cosx / sinx - cosx) =

(sinx - cosx) / cosx  ×  (sinx + cosx) / (sinx - cosx) =

(sinx + cosx) / cosx     (since sinx - cosx and sinx - cosx cancel each other)

= (sinx / cosx) + (cosx/cosx)

= tanx + 1