- #1

trollcast

Gold Member

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- 13

## Homework Statement

Show that:

$$\tan x\sec^4x\equiv\tan x\sec^2x + \tan^3x\sec^2x$$

## Homework Equations

Trig identities / formulae

## The Attempt at a Solution

I've got 2 different starts for it but I'm stuck after a few steps with both of them:

Attempt 1:

$$\tan x \sec^4 x$$

$$\frac{\tan x}{\cos^4 x}$$

$$\frac{\frac{\sin x}{\cos x}}{\cos^4 x}$$

$$\frac{\sin x \cos^4 x}{\cos x}$$

$$\sin x \cos^3 x$$

And then I can't think on anything else for this one.

Attempt 2:

$$\tan x \sec^4 x$$

$$\tan x (\tan^2 x + 1)^2$$

$$\tan x (\tan^4 x + 2\tan^2 x + 1)$$

$$\tan^5 x + 2\tan^3 x + \tan x$$

This one looks a bit closer since its got the higher power tans in it but I can't see where to get the sec terms from?