Question

evaluate sin45°/sec30°+cosec30°​

Answer 1

Answer:

$sin \: 45 = \frac{1}{ \sqrt{2} } \\ sec \: 30 = \frac{2}{ \sqrt{3} } \\ cosec \: 30 = 2 \\ now \: \\ \frac{sin \: 45}{sec \: 30} + cosec \: 30 = \frac{ \frac{1}{ \sqrt{2} } }{ \frac{2}{ \sqrt{3} } } + 2 \\ = \frac{ \sqrt{3} }{2 \sqrt{2} } + 2$

Answer 2

Answer:

$\frac{sin \ 45^0}{sec \ 30^0} +cosec \ 30^0$ = $\frac{\sqrt{6}+8 }{4}$

Step-by-step explanation:

To find,

$\frac{sin \ 45^0}{sec \ 30^0} +cosec \ 30^0$

Solution:

Recall the formulas

sin 45° = $\frac{1}{\sqrt{2} }$

sec 30° = $\frac{2}{\sqrt{3} }$

cosec 30° = 2

By substituting the values in the equation we get

$\frac{sin \ 45^0}{sec \ 30^0} +cosec \ 30^0$

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

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

= $\frac{\sqrt{3} + 4\sqrt{2} }{2\sqrt{2} }$

To rationalize the denominator, we should multiply the numerator and denominator with the rationalizing factor.

The rationalizing factor is √2

$\frac{\sqrt{3} + 4\sqrt{2} }{2\sqrt{2} } = \frac{\sqrt{3} + 4\sqrt{2} }{2\sqrt{2} }X\frac{\sqrt{2} }{\sqrt{2} }$

= $\frac{\sqrt{6} + 4\sqrt{4} }{2\sqrt{4} }$

= $\frac{\sqrt{6} + 4X2 }{4}$

= $\frac{\sqrt{6}+8 }{4}$

∴ $\frac{sin \ 45^0}{sec \ 30^0} +cosec \ 30^0$ = $\frac{\sqrt{6}+8 }{4}$

#SPJ3