From Pythagoras on a right triangle: sin2θ+cos2θ=1\sin^2\theta + \cos^2\theta = 1sin2θ+cos2θ=1. Dividing by cos2θ\cos^2\thetacos2θ gives tan2θ+1=sec2θ\tan^2\theta + 1 = \sec^2\thetatan2θ+1=sec2θ; dividing by sin2θ\sin^2\thetasin2θ gives 1+cot2θ=csc2θ1 + \cot^2\theta = \csc^2\theta1+cot2θ=csc2θ.