# Help With Inequalities Q Cambridge (1 Viewer)

#### hmim

##### Member
Can someone assist with 14 b) and explain the solution, please?

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#### jimmysmith560

##### Le Phénix Trilingue
Moderator
Would the following working help?

$\bg_white \tan x\le \sec ^2x-1$

$\bg_white \tan x\le \tan ^2x$

$\bg_white 0\le \tan ^2x-\tan x$

$\bg_white 0\le \tan x\left(\tan x-1\right)$

This is when $\bg_white \tan x\ge 0$ and $\bg_white \tan x\ge 1$ or when $\bg_white \tan x\le 0$ and $\bg_white \tan x-1\le 0$, making $\bg_white \tan x\le 1$.

The first solution is when $\bg_white \tan x\ge 1$, this is when $\bg_white \frac{\pi }{4}\le x<\frac{\pi }{2}$.

The second solution is when $\bg_white \tan x\le 0$, this is when $\bg_white -\frac{\pi }{2}.

#### hmim

##### Member
Would the following working help?

$\bg_white \tan x\le \sec ^2x-1$

$\bg_white \tan x\le \tan ^2x$

$\bg_white 0\le \tan ^2x-\tan x$

$\bg_white 0\le \tan x\left(\tan x-1\right)$

This is when $\bg_white \tan x\ge 0$ and $\bg_white \tan x\ge 1$ or when $\bg_white \tan x\le 0$ and $\bg_white \tan x-1\le 0$, making $\bg_white \tan x\le 1$.

The first solution is when $\bg_white \tan x\ge 1$, this is when $\bg_white \frac{\pi }{4}\le x<\frac{\pi }{2}$.

The second solution is when $\bg_white \tan x\le 0$, this is when $\bg_white -\frac{\pi }{2}.
Thanks!