Question

$\star \: \sf \underline{Evaluate } :-$

$\large\sf \frac{sin \: 30°}{cot \: 45°} + \frac{tan \: 45°}{cos \: 60°} - \frac{cosec \: 60°}{sec \: 30°}$

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Answer 1

$\color{blue} \star\large \sf \: \underline{\pink{Solution}} : -$

$\large \boxed{\sf \frac{sin \: 30°}{cot \: 45°} + \frac{tan \: 45°}{cos \: 60°} - \frac{cosec \: 60°}{sec \: 30°}}$

We know that :

$\sf \: sin \: 30° = \large\frac{1}{2}$

$\sf \: tan \: 45° = 1$

$\sf \: cosec \: 60° = \large \frac{2}{ \sqrt{3} }$

$\sf \: cot \: 45° = 1$

$\sf \: cos \: 60° = \large \frac{1}{2}$

$\sf \: sec \: 30° = \large \frac{2}{3}$

So,

$\boxed{ \sf = \large \cancel{\frac{ \: \: \frac{1}{2} + 1 - \frac{2}{ \sqrt{3} } }{ \: \: \: 1 + \frac{1}{2} - \frac{2}{ \sqrt{3} } \: \: } } = 1}$

$\:$

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