First slide

Trigonometric equations

Question

If A and B be acute positive angles satisfying $3 \sin^{2} A + 2 \sin^{2} B = 1, 3 \sin 2 A - 2 \sin 2 B = 0$ then

Moderate

A

$B = \frac{π}{4} - \frac{A}{2}$
B

$A = \frac{π}{4} - 2 B$
C

$B = \frac{π}{2} - \frac{A}{4}$
D

$A = \frac{π}{4} - \frac{B}{2}$

Solution

$\begin{array}{l} \sin 2 B = (3 / 2) \sin 2 A, \cos 2 B = 3 \sin^{2} A \\ \Rightarrow \tan 2 B = \cot A \Rightarrow \tan A \tan 2 B = 1 \\ \Rightarrow A + 2 B = π / 2 \\ \Rightarrow B = π / 4 - A / 2 \end{array}$

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