Question

Please help - trig identity

Answer 1

Explanation:

`LHS=cosec(x)-cosec(x)cos^(2) (x)\\\\LHS=cosec(x)-cosec(x)(1-sin^(2) (x))\\\\LHS=cosec(x)-cosec(x)+cosec(x)*sin^(2) (x)\\\\LHS=cosec(x)-cosec(x)+cosec(x)(1)/(cosec^(2)(x) ) \\\\LHS=cosec(x)-cosec(x)+(1)/(cosec(x) )\\\\LHS=(cosec^(2)(x)-cosec^(2)(x)+1 )/(cosec(x)) \\\\LHS=(1)/(cosec(x)) \\\\LHS=sin(x)=RHS`

Hence,LHS=RHS proved