Question

(1-sec²A)(cosec²-1)​

Answer 1

Step-by-step explanation:

We know the identities that,

Sin² A + Cos² A = 1

Sec² A - Tan² A = 1

Cosec² A - Cot² A = 1

So, According to the question,

( Sec² A - 1 ) ( Cosec² A - 1 ) = 1

LHS :

According to identity,

Sec² A - Tan² A = 1

=> Sec² A - 1 = Tan² A

Similarly,

Cosec² A - Cot² A = 1

=> Cosec² A - 1 = Cot² A.

So substituting them in place of the question we get,

( Tan² A ) ( Cot² A )

We know that, Cot² A = 1 / Tan² A

Hence substituting Cot² A we get

Tan² A * 1 / Tan² A

=> Tan² A / Tan² A

=> 1

RHS :

=> 1

Hence LHS = RHS.

Hence proved.

Hope it helped :-)