Question

Sec x tan x(1-sin^2x)=sinx is this equation a trigonometric identity?

Answer 1

$\bf tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\qquad sec(\theta)=\cfrac{1}{cos(\theta)} \\\\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\ -------------------------------\\\\ %sec x tan x(1-sin^2x)=sinx sec(x)tan(x)[1-sin^2(x)]=sin(x)\\\\ -------------------------------\\\\ sec(x)tan(x)[1-sin^2(x)]\implies \cfrac{1}{\underline{cos(x)}}\cdot \cfrac{sin(x)}{\underline{cos(x)}}\cdot \underline{cos^2(x)}\implies sin(x)$