First slide

Trigonometric equations

Question

If the equation $\tan^{4} x - 2 \sec^{2} x + a^{2} = 0$ has at least one solution, then sum of all possible integral values of ‘a’ is equal to

Moderate

A

0
B

4
C

2
D

3

Solution

$\tan^{4} x - 2 (\tan^{2} x + 1) + a^{2} = 0$
$\Rightarrow \tan^{4} x - 2 \tan^{2} x + 1 = 3 - a^{2}$
$\Rightarrow {(\tan^{2} x - 1)}^{2} = 3 - a^{2} \geq 0$
$\Rightarrow a^{2} \leq 3 \Rightarrow - \sqrt{3} \leq a \leq \sqrt{3}$
$\Rightarrow$ Integral values of ‘a’ are -1, 0, 1

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App