Question

cos 45°/sec 30°+cosec 30°​

Answer 1

Hope it may help you .....

Answer 2

$\sf\large\frac{cos\:45}{sec\:30+cosc\: 30}$

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∵ ( cos 45 = 1/√2

sec 30 = 2/√3

csc 30 = 2 )

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by substituting the values :-

⇒ $\sf\frac{\frac{1}{\sqrt{2}}}{(\frac{2}{\sqrt{3}})+(\frac{2}{1})}= \frac{\frac{1}{\sqrt{2}}}{\frac{2+2 \sqrt{3}}{\sqrt{3}}}$

(we will interchange the places of √3 and 1 so as not to get the value in negative form)

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

( Rationalizing the denominator because the final value must not be irrational )

⇒$\sf\frac{\sqrt{3}}{2\sqrt{2}(\sqrt{3} + 1)}\times\frac{\sqrt{2}(\sqrt{3}-1)}{\sqrt{2}(\sqrt{3}-1)}$

⇒$\sf\frac{\sqrt{6}(\sqrt{3}-1)}{4(({\sqrt{3})}^{2}-({1)}^{2}}$

⇒ $\sf\frac{\sqrt{18} -\sqrt{6}}{4(2)}$

⇒$\sf\frac{\sqrt{2\times3\times 3}- \sqrt{2\times3}}{8}$

⇒ $\sf\boxed{\frac{3\sqrt{2}-\sqrt{6}}{8}}$