First slide

Trigonometric equations

Question

The solution of $4 \sin^{2} x + \tan^{2} x + {cosec}^{2} x + \cot^{2} x - 6 = 0$ is $(n \in Z)$

Moderate

A

$nπ \pm \frac{π}{4}$
B

$2 nπ \pm \frac{π}{4}$
C

$nπ + \frac{π}{3}$
D

$nπ - \frac{π}{6}$

Solution

$\begin{array}{l} (2 \sin x - cosec x)^{2} + (\tan x - \cot x)^{2} = 0 \\ \Rightarrow \sin^{2} x = \frac{1}{2} and \tan^{2} x = 1 \\ \Rightarrow x = nπ \pm \frac{π}{4}, n \in Z \end{array}$

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