Question

Simplify the function: tan⁻¹ $(\frac{sin x}{1 + cos x})$.

Answer 1

Answer: The answer is to this question is " x/2"

Explanation:

I have used the following formulas to solve it.

• Double angle Identity
• Half Angle Identity

Given that

$tan^{-1}(\frac{sinx}{1+cosx})\\\\=tan^{-1}(\frac{2sin(x/2).cos(x/2)}{2cos^{2}(x/2) })\\\\=tan^{-1}(\frac{sin(x/2)}{cos(x/2) })\\\\=tan^{-1}(tan\frac{x}{2} )\\\\=\frac{x}{2}$

Hope that it will help you.