Math, asked by ananyacr27, 10 months ago

Prove that (sec A + tan A)^2 = cosec A + 1 / cosec A - 1

Answers

Answered by Anonymous
9

To Prove :

⇒ (sec A + tan A )² = cosec A + 1 / cosec A - 1

Proof :

On solving L.H.S

⇒ ( sec A + tan A )²

⇒ ( 1 / cos A + sin A / cos A )²

⇒ [ (1 + sin A ) / cos A ]²

⇒ ( 1 + sin A)² / ( 1 - sin² A )

⇒ ( 1 + sin A ) ( 1 + sin A ) / ( 1 + sin A ) ( 1 - sin A )

⇒ ( 1 + sin A ) / ( 1 - sin A )

⇒ ( 1 + 1 / cosec A) / ( 1 - 1 / cosec A )

⇒ ( 1 + cosec A ) / ( 1- cosec A )

L.H.S = R.H.S

Hence proved

Answered by Anonymous
1

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