Question

Evaluate cos45°/sec30°+cosec30°​ plz anyone give the right answer​

Answer 1

$\large \sf \: {Evaluate \longrightarrow \: \large \dfrac{cos45 \degree}{(sec30 \degree+cosec30 \degree)}}$

$\sf \: \large\dfrac{ \dfrac{1}{\sqrt{2}}} {\dfrac{ 2 }{ \sqrt{3} } \: + \: \dfrac{2}{1} }$

$\sf \: \large \: \dfrac{1}{ \sqrt{2} } \: \div \: \dfrac{2 \: + \: 2 \: \sqrt{3} }{ \sqrt{3} }$

$\sf \: \large \: \dfrac{1}{ \sqrt{2} } \: \times \: \dfrac{ \sqrt{3} }{ 2 \: + \: 2 \: \sqrt{3} }$

$\sf \large\dfrac{1}{\sqrt{2}}\times \dfrac{\sqrt{3}}{2(1+\sqrt{3})}$

$\sf \large\dfrac{\sqrt{2}}{\sqrt{2}\times \sqrt{2}} \times \dfrac{\sqrt{3}\times (\sqrt{3}-1)}{2(\sqrt{3}+1)(\sqrt{3}-1)}$

$\sf \large \dfrac{\sqrt{6}(\sqrt{3}-1)}{4\left(\big(\sqrt{3}\big)^{2}-1^{2}\right)}$

$\sf \large\dfrac{\sqrt{6}(\sqrt{3}-1)}{4(3-1)}$

$\sf \large\dfrac{\sqrt{6}(\sqrt{3}-1)}{8}$

$\sf \large \: \dfrac{3 \sqrt{2} \: - \: \sqrt{6} }{8}$

$\sf \red { Extra \: Information : }$ ↴

$\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0 \end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}$