First slide

Trigonometric transformations

Question

The values of the expression $\frac{1 - 4 \sin 10^{0} \sin 70^{0}}{2 \sin 10^{0}}$

Moderate

A

$2$
B

$\frac{1}{2}$
C

$1$
D

$\frac{1}{3}$

Solution

$\sin 70^{0} = \cos 20^{0}$ and use $2 \sin A \cos B = \sin (A + B) + \sin (A - B)$
$\frac{1 - 2 [\sin 30^{0} - \sin 10^{0}]}{2 \sin 10^{0}} = 1.$

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