Question

a
Evaluate (sec²a-1) (cosec² a-1)​

Answer 1

Answer:

Step-by-step explanation:

We know that

Sin² A + Cos² A = 1

Sec² A - Tan² A = 1

Cosec² A - Cot² A = 1

Question,

(Sec² A - 1) (Cosec² A - 1) = 1

Solving LHS :

=Sec² A - Tan² A = 1

=Sec² A - 1 = Tan² A

= Cosec² A - Cot² A = 1

= Cosec² A - 1 = Cot² A.

And Substituting them in place of the question we get,

( Tan² A ) ( Cot² A )

We know that, Cot² A = 1 / Tan² A

Therefore Substituting Cot² A we get

=Tan² A * 1 / Tan² A  

=Tan² A / Tan² A

=1

Solving RHS :

=1

Hence proved LHS = RHS.

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