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  • Evaluate the following : cos 45 ^o / sec 30 ^o plus csc 30 ^o

1.     Evaluate the following :

    (iii)\: \frac{\cos 45^{o}}{\sec 30^{o}+\csc 30^{o}}

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\frac{\cos 45^{o}}{\sec 30^{o}+\csc 30^{o}}
we know the value of

 \cos 45 = 1/\sqrt{2} , \sec 30^0 = 2/\sqrt {3} and cosec \:30 =2,

After putting these values 
=\frac{\frac{1}{\sqrt{2}}}{\frac{2}{\sqrt{3}}+2}
=\frac{1/\sqrt{3}}{(2+2\sqrt{3})/ \sqrt{3}}
\\=\frac{\sqrt{3}}{2\sqrt{2}+2\sqrt{6}}\times\frac{2\sqrt{2}-2\sqrt{6}}{2\sqrt{2}-2\sqrt{6}}
\\=\frac{2\sqrt{6}-2\sqrt{18}}{-16}\\ =2\frac{\sqrt{6}-3\sqrt{3}}{-16} = \frac{3\sqrt{3}-\sqrt{6}}{8}

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manish

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