Question

prove that 1+cot2 theta/1+cosec2theta = cosec theta​

Answer 1

$1 +\frac{cot^2\theta}{(1+cosec\theta)} = cosec\theta$ is proved

Step-by-step explanation:

To Prove :

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

L.H.S

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

we know that,

$cosec^2\theta = 1 + cot^2\theta\\cot^2\theta = cosec^2\theta-1$........(2)

Substituting  equation (2)  in (1), we get

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

we know that a²-b²= (a+b)(a-b)

Hence,

$cosec^2\theta -1 = (cosec\theta+1)(cosec\theta-1)$

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

$1+cosec\theta-1$ = $cosec\theta$

L.H.S = R.H.S

Hence proved.

The correct question is

Prove that 1 +{cot^2\theta}\{(1+cosec\theta)} = cosec\theta

To Learn More.....

1. Show that (cosec theta-cot theta) 2 =1-cos theta/ 1+cos theta

https://brainly.in/question/3113609

2. Prove that (cosec theta+sin theta)(cosec theta-sin theta)=cot square theta+cos square theta

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