Question

sin theta/(1+cos theta) + (1+cos theta)/sin theta is equal to​

Answer 1

Answer:

2cosecθ

Step-by-step explanation:

$\frac{sin\theta}{1+cos\theta}$ + $\frac{1+cos\theta}{sin\theta}$

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

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

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

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

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

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

= 2*$\frac{1}{sin\theta}$

= 2cosecθ