Prove the trigonometric identity. cscx cosx/(tanx+cotx)=cos^2x

Answer 1

rework the left side

numerator cscxcosx = (1/sinx)cosx = cosx/sinx

denominator tanx + cotx = sinx/cosx + cosx/sinx = (sin^2x + cos^2x)/sinxcosx = 1/sinxcosx

the left side then becomes (cosx/sinx)/(1/sinxcosx) = (cosx/sinx)(sinxcosx) = cos^2x which = the right side