Question

cota/coseca-1+cota/coseca+1=2seca prove ​

Answer 1

Step-by-step explanation:

L.H.S.

= (cos A / sin A ) / (1/sin A + 1 ) + (1/sin A + 1 ) / (cos A / sin A )

= (cos A / sin A ) / ( 1+ sin A/ sin A) + ( 1+ sin A/ sin A) / (cos A / sin A )

= (cos A/ 1+ sin A) + (1+ sin A / cos A )

= cos2A + ( 1+ sin A)2 / cos ( 1+ sin A)

= cos2A + 1 + sin2A + 2 sin A / cos A( 1+ sin A)

= 1 + 1 + 2 sin A / cos A( 1+ sin A)

= 2 + 2 sin A / cos A( 1+ sin A)

= 2 ( 1+ sin A) / cos A( 1+ sin A)

= 2 / cos A

= 2 sec A = R.H.S

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Answer 2

$\frac{cota}{coseca - 1} + \frac{cota}{coseca + 1} \\ \\ = cota( \frac{coseca + 1 + coseca - 1}{ {cosec}^{2}a - 1 } ) \\ \\ = cota( \frac{2coseca}{ {cot}^{2} a} ) \\ \\ = 2 \frac{coseca}{cota} \\ \\ = 2seca$