Question

$\boxed{\underline{{\boxed{\textbf{Question}}}}}$

Q.Find the values of:-

$\mathtt{\bf{\underline{\red{Need\:full\explaination\:}}}}$



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Answer 1

• Before solving this question let's have a look on trigonometry table

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$\Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 75^{\circ} & \sf 90^{\circ} \\ \cline{1-6} \sin & 0 & \dfrac{1}{2 } & \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} & 1 \\ \cline{1-6} \cos & 1 & \dfrac{ \sqrt{ 3 }}{2} } & \dfrac{1}{ \sqrt{2} } & \dfrac{ 1 }{ 2 } & 0 \\ \cline{1-6} \tan & 0 & \dfrac{1}{ \sqrt{3} } & 1 & \sqrt{3} & \infty \\ \cline{1-6} \cot & \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } &0 \\ \cline{1 - 6} \sec & 1 & \dfrac{2}{ \sqrt{3}} & \sqrt{2} & 2 & \infty \\ \cline{1-6} \csc & \infty & 2 & \sqrt{2 } & \dfrac{ 2 }{ \sqrt{ 3 } } & 1 \\ \cline{1 - 6}\end{tabular}}$

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$\sf{\underline{\boxed{\huge{\blue{\mathsf{Solution}}}}}}$

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$\sf :\implies{\bold{ \dfrac{2 cos^2 45 + 3tan^ 2 30}{\sqrt{3} cos 30 + sin 30}}}$

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$\sf :\implies{\bold{ \dfrac{2 \times(\dfrac{1}{\sqrt 2})^2 + 3\times (\dfrac{1}{\sqrt{3}})^2}{\sqrt{3} \times\dfrac{\sqrt 3}{2} + \dfrac{1}{2}}}}$

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$\sf :\implies{\bold{ \dfrac{2 \times \dfrac{1}{2} + 3\times\dfrac{1}{3}}{ \dfrac{3}{2} + \dfrac{1}{2}}}}$

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$\sf :\implies{\bold{ \dfrac{1 + 1}{\dfrac{3 + 1}{2}} }}$

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$\sf :\implies{\bold{ \dfrac{2 }{\dfrac{4}{2}}}}$

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$\sf :\implies{\bold{ \dfrac{2}{2}}}$

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$\sf :\implies{\bold{ 1 }}$

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$\sf{\red{\boxed{\bold{ \dfrac{2 cos^2 45 + 3tan^ 2 30}{\sqrt{3} cos 30 + sin 30} = 1 }}}}$

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