Question

The value of $(1-cosec^2A)tan^2A$ is:
(A) −1
(B) 0
(C) 1
(D) 2

Answer 1

Answer:

-1

Step-by-step explanation:

Hi,

Consider (1 - cosec²A)tan²A

= tan²A - cosec²A.tan²A

= tan²A - (1/sin²A)*(sin²A/cos²A)

= tan²A - 1/cos²A

= sin²A/cos²A - 1/cos²A

= (sin²A - 1)/cos²A

= -(1 - sin²A)/cos²A

= -1 (Since 1 - sin²A = cos²A).

Hope , it helps !

Answer 2

HELLO DEAR,

(1 - cosec²A)tan²A

= tan²A - cosec²A.tan²A

= tan²A - (1/sin²A)×(sin²A/cos²A)

= tan²A - 1/cos²A

= sin²A/cos²A - 1/cos²A

= (sin²A - 1)/cos²A

= -(1 - sin²A)/cos²A

= -cos²A/cos²A (Since 1 - sin²A = cos²A).

= -1

I HOPE IT'S HELP YOU DEAR,

THANKS