Question

Cos 60 + sin 45 -Cot 30 upon
tan 60 +sec 45° - Cosec 30​

Answer 1

$\huge\star{\tt{\underline{\underline{\red{Answer}}}}}\star$

Cos 60° = $\frac{1}{2}$

Sin45° = $\frac{1}{\sqrt{2}}$

Cot30° = $\frac{1}{\sqrt{3}}$

Tan60°= $\frac{1}{\sqrt{3}}$

sec45°= $\sqrt{2}$

cosec30°= 2

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Now putting these values

$\huge{\frac{cos 60 + sin45 - cot 30}{tan60 +sec45 -csc60}}$ the

$\implies$ $\large{\frac{\frac{1}{2} + \frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}}{\frac{1}{\sqrt{3}}+\sqrt{2} -2}}$

$\implies$ $\large{\frac{ \frac{ \sqrt{6} +2\sqrt{3} -2\sqrt{2} }{2\sqrt{6}}}{\frac{1 + \sqrt{6} -2\sqrt{3}}{\sqrt{3}}}}$

$\implies$ $\large{\frac{\sqrt{6} + 2\sqrt{3} - 2\sqrt{2} x \sqrt{3} }{ 2\sqrt{6} x 1 + \sqrt{6} -2\sqrt{3}}}$

$\implies$ $\large{\frac{ \sqrt{18} + 2 \sqrt{9} -2\sqrt{6}}{2\sqrt{6} + 2\sqrt{36} -4\sqrt{18}}}$

$\implies$ $\huge{\boxed{\frac{3\sqrt{2} + 6 -2\sqrt{6}}{2\sqrt{6} +12 - 12\sqrt{2}}}}$

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