Question

Evaluate Cos45°÷Sec30°+Cosec30°​

Answer 1

$\huge\green{★ SOLUTION : }$

Given that,

$\frac{ \cos \: 45 }{ \sec \: 30 + \csc \: 30 }$

Values of

• cos 45° = 1/√2
• sec 30° = 2/√3
• cosec 30° = 2

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

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

$⟹ \frac{1}{ \sqrt{2} } \times \frac{ \sqrt{3} }{2 + 2 \sqrt{3} }$

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

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

$⟹ \frac{ \sqrt{6}( \sqrt{3} - 1) }{4( {( \sqrt{3}) }^{2} - {(1)}^{2} ) }$

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

$⟹\frac{ \sqrt{6}( \sqrt{3} - 1) }{4(2)}$

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

$\boxed{∴ \: \frac{ \cos \: 45}{ \sec30 \: + \csc \: 30 } = \frac{ \sqrt{6} ( \sqrt{3} - 1)}{8} }$

Step-by-step explanation:

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