prove the identity 12cotx tanxcsc2xSolutionSolution prove t

prove the identity

1/2(cotx + tanx)=csc2x

Solution

Solution:

prove the identity

1/2(cotx + tanx) = csc2x

LHS

cot(x) = cos(x)/sin(x)

tan(x) = sin(x)/cos(x)

(cot(x) + tan(x)) = {cos(x)/sin(x) + sin(x)/cos(x)}
                        = (cos^2(x) + sin^2(x))/sin(x)cos(x)
                        = 1/sin(x)cos(x)
                        = 2/2sin(x)cos(x)
                         = 2/sin(2x)
(cot(x) + tan(x)) = 2csc(2x)

So

1/2(cotx + tanx)=csc(2x) RHS