Question

10. Determine whether the following represents an identity. cos x sin x tan x + cos²x = 1

Answer 1

Answer:

yes

Step-by-step explanation:

Given that $\cos x\sin x\tan x+\cos^2x=1$

Substitute $\tan x=\frac{\sin x}{\cos x}$, we obtain:

$\cos x\sin x\frac{\sin x}{\cos x}+\cos^2 x=1$

Simplifying this, we get:

$\sin x\sin x+\cos^2x=1$

This is equivalent to:

$\sin^2x+\cos^2x=1$