Question

Prove that sinΦ/1+cosΦ + 1+cosΦ/sinΦ = 2 cosecΦ​

Answer 1

Answer:

Step-by-step explanation:

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

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

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