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Cos45/sec30 +cosec30

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Cos45/sec30 +cosec30

Posted by Takshi Shukla 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 2 months ago

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

{tex}=\frac{\frac{1}{\sqrt{2}}}{\frac{2}{\sqrt{3}}+2}{/tex}

{tex}=\frac{\frac{1}{\sqrt{2}}}{\frac{2+2\sqrt{3}}{\sqrt{3}}}{/tex}

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

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

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

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

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

Therefore,

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

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CBSE > Class 10 > Mathematics