Help With Inequalities Q Cambridge (1 Viewer)

hmim · Feb 3, 2023

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

jimmysmith560 · Feb 3, 2023

Would the following working help?

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

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

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

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

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

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

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

hmim · Feb 6, 2023

jimmysmith560 said:
Would the following working help?

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

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

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

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

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

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

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

Thanks!

Help With Inequalities Q Cambridge (1 Viewer)

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