Question

Find the value of sinθ/(1+cosθ) + (1+cosθ)sinθ​

Answer 1

$\frac{ \sin(x) }{(1 + \cos(x)) } + \frac{(1 + \cos(x)) }{ \sin(x) } \\ \\ = \frac{ { \sin^{2} (x) +(1 + \cos(x))^{2} } }{ \sin(x)(1 + \cos(x)) } \\ \\ = \frac{\sin^{2} (x) + \cos^{2} (x) + 1 + 2 \cos(x) }{ \sin(x)(1 + \cos(x)) } \\ \\ = \frac{1 + 1 + 2 \cos(x) }{ \sin(x)(1 + \cos(x)) } \\ \\ = \frac{2+ 2 \cos(x) }{ \sin(x)(1 + \cos(x)) } \\ \\ = \frac{2(1 + \cos(x)) }{ \sin(x)(1 + \cos(x)) } \\ \\ = \frac{2}{ \sin(x) }$