Trigonometric EquationMedium
Question
The value of $cosec10^{\circ} - \sqrt{3}sec10^{\circ}$ is equal to:
Options
A.4
B.2
C.8
D.6
Solution
$= \frac{1}{sin10^{\circ}} - \frac{\sqrt{3}}{cos10^{\circ}}$
$${= \frac{cos10^{\circ} - \sqrt{3}sin10^{\circ}}{sin10^{\circ}cos10^{\circ}} }{= 4\left\lbrack \frac{\frac{1}{2}cos10^{\circ} - \frac{\sqrt{3}}{2}sin10^{\circ}}{2sin10^{\circ}cos10^{\circ}} \right\rbrack }{= 4\left\lbrack \frac{sin\left( 30^{\circ} - 10^{\circ} \right)}{sin20^{\circ}} \right\rbrack }{= 4}$$
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