Math, asked by Ansi1, 1 year ago

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

Answers

Answered by mysticd
885

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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Answered by Acharyavalmiki
96

Step-by-step explanation:

Given in attached Photo

Attachments:
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