Question

kindly solve this question
Coth²x - cosech²x=1

Answer 1

Consider a right angled triangle, right angle at B

so AC is the hypotenuse. Let the angle x be at A, BC is the opposite side & AB is the adjacent side.

cotx = adjacent side to x / opposite side to x = AB/BC

cosec x = hypotenuse / opposite side to x

= AC/BC



Now

cot²x-cosec²x

=(AB/BC)²-( AC/BC )²

=AB²-AC²/BC²

=-(AC²-AB²)/BC²

=-BC²/BC²

=-1

So finally cot²x-cosec²x =-1

hope helped!