Question

Evaluate... cos 45 /( sec 30 +cosec 30)

Answer 1

Answer:

$Value \: of \:\frac{cos45}{(sec30+cosec30)}\\=\frac{\sqrt{6}(\sqrt{3}-1)}{8}$

Step-by-step explanation:

$Value \: of \:\frac{cos45}{(sec30+cosec30)}$

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

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

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

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

$=\frac{\sqrt{6}(\sqrt{3}-1)}{4\left(\big(\sqrt{3}\big)^{2}-1^{2}\right)}$

$=\frac{\sqrt{6}(\sqrt{3}-1)}{4(3-1)}$

$=\frac{\sqrt{6}(\sqrt{3}-1)}{8}$

Therefore,

$Value \: of \:\frac{cos45}{(sec30+cosec30)}\\=\frac{\sqrt{6}(\sqrt{3}-1)}{8}$

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Answer 2

Step-by-step explanation:

Given in attached Photo