Question

Cos (90-theta) • cosec90-theta) =tano. How?​

Answer 1

Answer:

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TRIGONOMETRY IDENTITIES TO BE USED IN THE QUESTION :-

For any right angled triangle with one angle α ,

• $\cos (90 - \alpha ) = \sin \alpha$  or  $\sin(90 - \alpha ) = \cos\alpha$

• $cosec \: (90 - \alpha ) = \sec\alpha$   or  $\sec(90 - \alpha ) = cosec\:\alpha$

SOME GENERAL TRIGNOMETRIC FORMULAS :-

• $\sin \alpha = \frac{1}{cosec \: \alpha }$  or  $cosec \: \alpha = \frac{1}{\sin \alpha }$

• $\cos \alpha = \frac{1}{\sec \alpha }$  or  $\sec \alpha = \frac{1}{\cos \alpha }$

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Now , lets come to the question.

In a right angled triangle , let one angle be α (in place of theta) .

So , lets solve L.H.S.

$\cos (90 - \alpha ) \times cosec(90 - \alpha )$

$=> sin\alpha \times \sec\alpha$

$=> \sin\alpha \times \frac{1}{\cos\alpha }$

$=> \frac{\sin\alpha }{\cos\alpha }$

$=> \tan\alpha$ = R.H.S.

∴ L.H.S. = R.H.S. (Proved)