Or tan²θ = (x² 1/16x² – 1/2) or tan²θ = x² 1/16x² – 1/2 or tan²θ = (x – 1/4x) 2 or tanθ = (x1/4x) or – (x1/4x) when tanθ = (x1/4x) we get secθ tanθ = x 1/4x x 1/4x = 2x when tanθ = (x – 1/4x) secθtanθ = (x 1/4x) – (x – 1/4x) = 1/2x Hence secθ tanθ = (x1/4x) – (x1/4x) = 1/2xYes, sec 2 x−1=tan 2 x is an identity sec 2 −1=tan 2 x Let us derive the equation We know the identity sin 2 (x)cos 2 (x)=1 ——(i) Dividing throughout the equation by cos 2 (x) We get sin 2 (x)/cos 2 (x) cos 2 (x)/cos 2 (x) = 1/cos 2 (x) We know that sin 2 (x)/cos 2 (x)= tan 2 (x), and cos 2 (x)/cos 2 (x) = 1 So the equation (i) after substituting becomes tan 2 (x) 1= 1 1tanx*tan2x = sec 2x LS =1 (sin x/cos x)(sin 2x/ cos 2x) =1 (sin x/cos x)(2sin x* cos x)/ cos 2x) =12sin^2(x)/(cos 2x) ={cos(2x) 2sin^2(x)}/cos (2x)
Proof Tan 2 1 Sec 2 Youtube
