First slide

Trigonometric Identities

Question

If $2 \sin^{2} A - \cot^{2} B = 1$ then sin A sin B =

Moderate

A

$- \frac{1}{\sqrt{2}}$
B

$\pm \frac{1}{\sqrt{2}}$
C

$\frac{1}{\sqrt{2}}$
D

$\frac{- 1}{2 \sqrt{2}}$

Solution

$2 \sin^{2} A - \cot^{2} B = 1 \Rightarrow 2 \sin^{2} A - \frac{\cos^{2} B}{\sin^{2} B} = 1 \Rightarrow 2 \sin^{2} A \sin^{2} B = \sin^{2} B + \cos^{2} B = 1 \Rightarrow \sin A \sin B = \pm \frac{1}{\sqrt{2}}$

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