Question

prove that 1+ cot square theta / 1+cosec theta =1/sin theta

Answer 1

if my answer is helpful for you then please mark as brainliest

Answer 2

Answer:

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

Step-by-step explanation:

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

Therefore,

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

•••♪