Question

What basic trigonometric identity would you use to verify that sin x cos x tan x = sin^2 x?

Answer 1

Use basic trigonometric identity

`\tan x =(\sin x)/(\cos x)`

Explanation:

Use basic trigonometric identity

`\tan x =(\sin x)/(\cos x)`

Substitute it into the expression

`\sin x\cos x\tan x=\sin ^2 x:`

`\\ \\\sin x\cdot \cos x\cdot (\sin x)/(\cos x)\\ \\=(\sin x\cdot \cos x\cdot \sin x)/(\cos x)\\ \\=(\sin x\cdot \sin x)/(1)\ \ [\text{Cancelled}\ \cos x]\\ \\=\sin^2x`