Question

(Coseco+1) (coseco -1)=1/tan^2theta proove. ​

Answer 1

Answer:

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Answer 2

Given :

$(\csc +1)(\csc-1)=\frac{1}{\tan^2}$

To Prove :

$\text{RHS = LHS}$

Identity Used :

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

Solution :

$\implies( \csc^2 \theta+1)(\csc^2-1)$

$\implies \csc^2\theta-\csc\theta+csc\theta -1$

$\implies \csc^2\theta-1$

$\implies \cot^2\theta \:\:(\because \csc^2\theta-1=\cot^2\theta)$

$\implies \frac{1}{\tan^2\theta} \:\:(\because \:\:\tan \:\:and\:\:\cot\:\: \text{are inverse each other}$

Hence Proved.

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Some More Identities :

$\sin^2 x+ \cos^2 x=1$

$\tan^2x+1=\sec^2x$

$\cot^2x+1=\csc^2$