Question

3) prove the following
(Trigonometric identities)

Answer 1

In both of them ypu can just cross multiply.

And the resultant is a known identity for being equal to 1.

=> cosec x - cot x = 1 / (cosec x + cot x)

=> (cosec x - cot x)(cosec x + cot x) = 1

=> cosec ² x - cot ² x = 1 {known to be equal to one}

=> 1 = 1 Hence Proved.

The same can be done for the other one and be rearranged.

cross multiplying you'll get

=> (cosec x + 1)(cosex - 1) = cot x * cot x

=> cosex ² x - 1 = cot ² x

=> cosec ² x - cot ² x = 1

=> 1 = 1 Hence Proved.