Question

1 + cot square theta upon 1 + cosec theta is equal to 1 by sin​

Answer 1

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Answer 2

Answer with Step-by-step explanation:

Given:

LHS

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

We know that

$cot^2\theta=cosec^2\theta-1$

Using the formula

$1+\frac{cosec^2\theta-1}{1+cosec\theta}$

$1+\frac{(cosec\theta+1)(cosec\theta-1)}{1+cosec\theta}$

Using the formula

$a^2-b^2=(a+b)(a-b)$

$1+cosec\theta-1$

$=cosec\theta$

We know that

$cosec\theta=\frac{1}{sin\theta}$

Using the formula

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

LHS=RHS

Hence, proved.

#Learn more:

https://brainly.in/question/3048117:Answered by Chirag