cos45 degree divided by sec 30 degree plus cosec 30 degree .... hw do u solve it in simple way ... nd hw do v rationalise d denominator

Question

cos45 degree divided by sec 30 degree plus cosec 30 degree hw do
u solve it in simple way nd hw do v rationalise d denominator

Ajanta Trivedi · Accepted Answer

We can't leave at the point you have marked because root in denominator cannot be the final answer.
If there is root in the denominator, then we need to rationalize it.
the given trigonometric expression is:

$\frac{\cos 45}{\sec 30 + \cos e c 30} = \frac{1 / \sqrt{2}}{2 / \sqrt{3} + 2} = \frac{1}{\sqrt{2}} * \frac{1}{\frac{2 + 2 \sqrt{3}}{\sqrt{3}}} = \frac{1}{\sqrt{2}} * \frac{\sqrt{3}}{2 (1 + \sqrt{3})}$ rationalizing the denominator

$= \frac{1}{\sqrt{2}} * \frac{\sqrt{2}}{\sqrt{2}} * \frac{\sqrt{3}}{2 (1 + \sqrt{3})} * \frac{(1 - \sqrt{3})}{(1 - \sqrt{3})} = \frac{\sqrt{2}}{2} * \frac{\sqrt{3}}{2} * \frac{(1 - \sqrt{3})}{1 - 3} = \frac{\sqrt{6}}{4} * \frac{(1 - \sqrt{3})}{- 2} = - \frac{\sqrt{6} - 3 \sqrt{2}}{8} = \frac{3 \sqrt{2} - \sqrt{6}}{8}$

hope this helps you.

cheers!!