Question

cos 45°/ sec 30° + cosec 30°​

Answer 1

$\huge\mathcal\color{teal}{Answer :- }$

Refer the attachment above ...

Hope it Helps !!

Answer 2

Find the value of cos45°/sec30° + cosec30°

Answer :-

Firstly we have to find the values of the trig. functions. The angles are already given and they're also special angles, so we already know the ratio.

cos45 = 1/√2

sec30 = 1/cos30 = 2/√3

cosec30 = 1/sin30 = 2/1

Now let us evaluvate.

$\frac{1}{ \sqrt{2} } \times \frac{2}{ \sqrt{3} } + 2$

$\frac{1}{1} \times \frac{ \sqrt{2} }{ \sqrt{3} } + 2$

(because we are cancelling √2 and 2)

$\frac{ \sqrt{2} }{ \sqrt{3} } + 2$

Take LCM

$\frac{ \sqrt{2} + 2 \sqrt{3} }{ \sqrt{3} }$

Now you can rationalize the denominator if you want to,

$\frac{( \sqrt{2} + 2 \sqrt{3}) \sqrt{3} }{ \sqrt{3} \times \sqrt{3} }$

You get the final answer as

$\frac{ \sqrt{6} + 6}{3}$