Question

10. Determine whether the following represents an identity.

cos x sin x tan x + cos²x = 1

Answer 1

yes

Explanation:

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

Substitute
`\tan x=(\sin x)/(\cos x)`, we obtain:

`\cos x\sin x(\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`