Question

evaluate:sin^2 30°+ cos^2 30°/cos 90°+cot^2 60°​

Answer 1

Answer:

$\sf{ \dfrac{{sin}^{2} {30}^{\circ} + {cos}^{2} {30}^{\circ}}{cos \: {90}^{\circ} + {cot}^{2} {60}^{\circ}} = \bf{3}}$

Step-by-step explanation:

$\begin{array}{ |c|c|c|c|c|c|} \sf\angle A & \sf{0}^{ \circ} & \sf{30}^{ \circ} & \sf{45}^{ \circ} & \sf{60}^{ \circ} & \sf{90}^{ \circ} \\ \\ \sf sin \: A & 0 & \dfrac{1}{2} & \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3} }{2} & 1 \\ \\ \sf cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \sf \: tan \: A & 0 & \dfrac{1}{ \sqrt{3} }& 1 & \sqrt{3} & \sf Not \: de fined \\ \\ \sf cosec \: A & \sf Not \: de fined & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } & 1 \\ \\ \sf sec \: A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \sf Not \: de fined \\ \\ \sf cot \: A & \sf Not \: de fined & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}$

$\sf{ \longrightarrow \: \dfrac{{sin}^{2} {30}^{\circ} + {cos}^{2} {30}^{\circ}}{cos \: {90}^{\circ} + {cot}^{2} {60}^{\circ}}}$

$\sf{ \longrightarrow \:} \: \dfrac{(\frac{1}{2})^{2} + ( \frac{ \sqrt{3} }{2})^{2}}{0 + ( \frac{1}{ \sqrt{3}})^{2}}$

$\sf{ \longrightarrow \:} \: \dfrac{\frac{1}{4} + \frac{3}{4}}{0 + \frac{1}{3}}$

$\sf{ \longrightarrow \:} \: \dfrac{\frac{4}{4}}{\frac{1}{3}}$

$\sf{ \longrightarrow \:} \: \dfrac{1}{\frac{1}{3}}$

$\sf{ \longrightarrow \:} \: 1 \times \dfrac{3}{1}$

$\sf{ \longrightarrow \:} 3$

$\therefore \: \sf{ \dfrac{{sin}^{2} {30}^{\circ} + {cos}^{2} {30}^{\circ}}{cos \: {90}^{\circ} + {cot}^{2} {60}^{\circ}} = \bf{3}}$