Question

Cos 45 degree upon sec 30 degree + cosec 30 degree evaluate

Answer 1

To find the value of:

$\mathsf{ \frac{cos45}{sec30 + cosec30} }$

From the trigonometric table,

cos45= 1/√2

sec30= 2/√3

cosec30=2

Substituting the values,we obtain:

$\sf{ \frac{ \frac{1}{ \sqrt{2} } }{ \frac{2}{ \sqrt{3} } + 2} } \\ \\ = \sf{ \frac{ \frac{1}{ \sqrt{2} } }{ \frac{2 + 2 \sqrt{3} }{ \sqrt{3} } } } \\ \\ = \sf{\frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2 + 2 \sqrt{3} }} \\ \\ = \boxed{ \sf{\frac{ \sqrt{3} }{2( \sqrt{2} + \sqrt{6}) }}}$

Answer 2

Step-by-step explanation:

Hi,

Cos 45° = 1/√2

Sec30° = 2/√3

Cosec30° = 2

Cos 45° / Sec 30° + Cosec 30°

1/√2 / 2/√3 + 2

1/√2 / 2 + 2√3 / √3

1/√2 + √3 / 2 + √3

√3 / √2 ( 2 + √3 )

√3/2√2 + √6

Hope it will help you :)