Question

prove that:

cosec theta(1+costheta) (cosectheta-cottheta)=1
plz solve this itz urgent​

Answer 1

Answer:

pls mark me as brainliest

Answer 2

Given:-

$f(\theta)=cosec\theta\times(1+cos\theta)\times(cosec\theta-cot\theta)$

To Prove:-

$f(\theta)=1$

Proof:-

Convert all the terms in $sin\theta and cos\theta$

$f(\theta)=\frac{1}{sin\theta}\left(1+cos\theta\right)\left(\frac{1}{sin\theta}-\frac{cos\theta}{sin\theta}\right)\\\\f(\theta)=\left(\frac{1}{sin\theta}+\frac{cos\theta}{sin\theta}\right)\left(\frac{1}{sin\theta}-\frac{cos\theta}{sin\theta}\right)\\\\f(\theta)=\left(\frac{1+cos\theta}{sin\theta}\right)\left(\frac{1-cos\theta}{sin\theta}\right)\\\\f(\theta)=\frac{1-cos^{2}\theta}{sin^{2}\theta}$

Use the identity $sin^{2}\theta+cos^{2}\theta=1$ to solve it.

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

Hence proved.