Question

If cot θ - cosec θ = p , then prove that cot θ + cosec θ = -p.

Answer 1

cot theeta - cosec theeta = p { given }

=> cosec theeta - cot theeta = -p ....... (i)

=> cosec² theeta = 1 + cot² theeta

=> cosec² theeta - cot² theeta = 1

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

=> ( cosec theeta + cot theeta ) ( -p ) = 1

=> ( cosec theeta + cot theeta ) = -1/p

hope it's helpful........