Question

help to prove this Question

Answer 1

abhi178 - The Sage

LHS = {cos(π+x).cos(-x)}/{sin(π-x).cos(π/2-x)}

we know,

cos(π+x) = -cosx

sin(π-x) = sinx

cos(-x) = cosx

cos(π/2 + x) = -sinx, use this above .

LHS = {(-cosx).cosx}/{sinx.(-sinx}

= cos²x/sin²x

= cot²x = RHS