Question

The value of the expression
[(sec2 theta - 1) (1 - cosec2 theta )] is :
(A) – 1 (B) 1 (C) 0 (D) 2​

Answer 1

Answer:

1, option ( B ) is right

Step-by-step explanation:

Given---> ( Sec²θ - 1 ) ( 1 - Cosec²θ )

To find---> Value of given expression.

Solution---> We know that

1 + tan²A = Sec²A

=> tan²A = Sec²A - 1

We know that,

1 + Cot²A = Cosec²A

=> Cot²A = Cosec²A - 1

Now returning to original problem

( Sec²θ - 1 ) ( Cosec²θ - 1 )

Putting Sec²θ - 1 = tan²θ and Cosec²θ - 1 = Cot²θ , we get.

= ( tan²θ ) ( Cot²θ )

We know that Cotθ = 1 / tanθ , using it here we get,

= tan²θ ( 1 / tan²θ )

tan²θ cancel out from numerator and denominator

= 1

Answer 2

Answer:

Option is (b) the correct..