Question

The value of $\frac{1}{sin{10}^0}-\frac{\sqrt{3}}{cos{10}^0}$is

• A. 2
• B. 1
• C. 4
• D. 3

Answer 1

The correct option is C 4

$\frac{1}{sin{10}^0}-\frac{\sqrt{3}}{cos{10}^0}$
Multiplying and dividing by 2
Denominator=$2sin{10}^{0}cos{10}^0$
$=sin{20}^0$
Therefore
$2/sin{20}^0(cos{10}^0-\sqrt{3}sin{10}^0)$
multiplying and dividing by 2 we get
$4/sin{20}^0(\frac{cos{10}^0}{2}-\frac{\sqrt{3}sin{10}^0}{2})$
$=\frac{4}{sin{20}^0}\left(sin\right({30}^0-{10}^0\left)\right)$
$=\frac{4}{sin{20}^0}\left(sin\right({20}^0\left)\right)$
$=4$
Hence answer is C