Question

(1-cos2tita) sec2tita = tan2tita

Answer 1

Answer:

$(1-cos^2\theta)sec^2\theta=tan^2\theta$

Step-by-step explanation:

$\text{Prove that:}(1-cos^2\theta)sec^2\theta = tan^2\theta$

$(1-cos^2\theta)sec^2\theta$

using

$\boxed{1-cos^2A=sin^2A}$

$=(sin^2\theta)sec^2\theta$

$=(sin^2\theta)(\frac{1}{cos^2\theta})$

$=\frac{sin^2\theta}{cos^2\theta}$

$=tan^2\theta$

$\implies\:\boxed{(1-cos^2\theta)sec^2\theta=tan^2\theta}$