Question

sin 30° + tan 45º - cosec 60°/
sec 30° + cos 60° + cot 45°
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Answer 1

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$\longrightarrow \sf \frac{ \sin 30° + \tan 45° - \cosec 60°}{ \sec 30° + \cos 60° + \cot 45°} \\ \\\longrightarrow \sf \dfrac{ \dfrac{1}{2} + 1 - \dfrac{2}{ \sqrt{3} } }{ \dfrac{2 }{ \sqrt{3}} + \dfrac{1}{2} + 1} \\ \\ \longrightarrow \sf \dfrac{ \dfrac{ \sqrt{3} + 2 \sqrt{3} - 4 }{2 \sqrt{3} } }{ \dfrac{4 + \sqrt{3} + 2 \sqrt{3} }{2 \sqrt{3} } } \\ \\ \longrightarrow \sf\frac{ \sqrt{3} + 2 \sqrt{3} - 4 }{4 + \sqrt{3} + 2 \sqrt{3} } \\ \\ \longrightarrow \sf\frac{3 \sqrt{3} - 4 }{3 \sqrt{3} + 4 } \times \frac{3 \sqrt{3} - 4}{3 \sqrt{3} - 4} \\ \\\longrightarrow \sf \frac{27 - 12 \sqrt{3} - 12 \sqrt{3} + 16 }{27 - 16} \\ \\ \longrightarrow \boxed{\sf \frac{43 - 24 \sqrt{3} }{11}}$

Answer 2

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