Question

Evaluate the statement :

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Answer 1

Question :

$\sf\red{2 \bigg({\frac{ \cos58° }{ \sin32° } \bigg)- \sqrt{3} \bigg(\frac{ \cos38° \: \csc52° }{ \tan15° \: \tan60° \: \tan75° }\bigg)}}$

Solution :

$\sf\bigg[{2\: \frac{ \cos90 - 32 }{ \sin32 }}\bigg]$

$\sf\bigg[{ - \sqrt{3} \frac{ \cos(90 - 52) \:\csc52 }{ \tan(90 \:-\: 75) \:\tan60 \:\tan75}\bigg]}$

$\sf\bigg[{2 \frac{ \sin32 }{ \sin32 }\bigg] - \bigg[\sqrt{3} \frac{ \sin52\: \frac{1}{ \sin52 } }{ \cot75\: \tan60 \:\frac{1}{ \cot75 }}\bigg]}$

$\sf{2 \times 1 - \sqrt{3} \bigg(\frac{1}{ \sqrt{3}}\bigg) = 2 - \sqrt{3} \times \frac{1}{ \sqrt{3}} }$

$\sf{2 - 1 = 1}$