First slide

Trigonometric equations

Question

Number of solutions of the equation $4 \sin^{2} x + \tan^{2} x$ $+ \cot^{2} x + {cosec}^{2} x = 6 in [0, π] is$

Moderate

A

0
B

2
C

4
D

8.

Solution

$\begin{array}{l} 2 \sin^{2} ((π / 2) \cos^{2} x) = 2 \sin^{2} ((π / 2) \sin 2 x) \\ or if (π / 2) \cos^{2} x = \pm (π / 2) \sin 2 x \\ or if either \cos x = 0 or \cos x = \pm 2 \sin x \\ and \cos x = 0 if x = (2 n + 1) π / 2 . \end{array}$

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