Question

Prove that :-
tan^2a.sec(90-a) - sin^2a.cosec^2(90-a) = 1

Answer 1

tan²a sec(90-a) - sin²a cosec²(90-a)

tan²a cosec a - sin²a sec²a

sin²a/ cos²a *1/sina - sin²a/cos²a

sina/cos²a - tan²a

tan a * seca -tan²a

Step-by-step explanation:

tan²a sec(90-a) - sin²a cosec²(90-a)

tan²a cosec a - sin²a sec²a

(tan a can be written as sin a/ cos a)

sin²a/ cos²a *1/sina - sin²a/cos²a

sina/cos²a - tan²a

(sin a/ cos a is tan a, 1/cos a is sec a.)

tan a * seca -tan²a