Question

solveeeeeeeeeeeee solveeee
no idiotic answer

Answer 1

Here is your answer :

R.H.S = 2 cosec A

L.H.S = [ tan A / ( 1 + sec A ) ] - [ tan A / ( 1 - sec A ) ]

Taking the L.C.M of denominator :

= [ tan A ( 1 - sec A ) - tan A ( 1 + sec A ) ] / [ ( 1 + sec A ) ( 1 - sin A ) ]

Taking tan A common in numerator,

= [ tan A ( 1 - sec A - 1 - sec A ) ] / [ ( 1 + sec A ) ( 1 - sec A ) ]

Using identity :

[ ( a + b ) ( a - b ) = a² - b² ]


= [ tan A ( -2 sec A ) ] / [ 1 - sec² A ] --- ( 1 )

Using identity :

=> sec² A - tan²A = 1

=> -tan² A = 1 - sec² A ------- ( 2 )

Plug the value of ( 2 ) in ( 1 ),

= [ -2 × tan A × sec A ] / ( - tan² A )

= ( 2 sec A ) / tan A

Using identity :

=> sec A = 1/cos A

And

=> tan A = sin A / cos A

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

= ( 2 / cos A ) × ( cos A / sin A )

= 2 / sin A

Using identity :

=> ( 1 / cosec A ) = sin A

= 2 / ( 1 / cosec A)

= 2 × cosec A

=> 2 cosec A = R.H.S

Proved

Hope it helps !!