Question

2) tan 30° sec 45° + tan 60° sec 30°​

Answer 1

$\mathtt{\huge{\underline{\bf{\pink{Answer:-}}}}}$

tan 30° sec 45° + tan 60° sec 30°

➝ $\dfrac{1}{ \sqrt{3} } \times \sqrt{2 } + \sqrt{3} \times \dfrac{2}{ \sqrt{3} }$

➝ $\cancel{\dfrac{1}{ \sqrt{3} } \times \sqrt{2 } } + \cancel{\sqrt{3} \times \dfrac{2}{ \sqrt{3} }}$

➝ $\frac{ \sqrt{2} + 2 \sqrt{3} }{ \sqrt{3} }$

$\Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 65^{\circ} & \sf 90^{\circ} \\ \cline{1-6} \sin & 0 & \dfrac{1}{2 } & \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} & 1 \\ \cline{1-6} \cos & 1 & \dfrac{ \sqrt{ 3 }}{2} } & \dfrac{1}{ \sqrt{2} } & \dfrac{ 1 }{ 2 } & 0 \\ \cline{1-6} \tan & 0 & \dfrac{1}{ \sqrt{3} } & 1 & \sqrt{3} & \infty \\ \cline{1-6} \cot & \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } &0 \\ \cline{1 - 6} \sec & 1 & \dfrac{2}{ \sqrt{3}} & \sqrt{2} & 2 & \infty \\ \cline{1-6} \csc & \infty & 2 & \sqrt{2 } & \dfrac{ 2 }{ \sqrt{ 3 } } & 1 \\ \cline{1 - 6}\end{tabular}}$