Question

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

Answer 1

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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 = (1)/(cosec \: \alpha )` or
  `cosec \: \alpha = (1)/(\sin \alpha )`

• 
  `\cos \alpha = (1)/(\sec \alpha )` or
  `\sec \alpha = (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 ) * cosec(90 - \alpha )`

`=> sin\alpha * \sec\alpha`

`=> \sin\alpha * (1)/(\cos\alpha )`

`=> (\sin\alpha )/(\cos\alpha )`

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

∴ L.H.S. = R.H.S. (Proved)