Question

if sin theta =cos theta find value of theta​

Answer 1

${\red {{\bold{ \huge \dag }}\bold {\huge{{\mathcal {\underline{Answer}}}} \dag}}}$

$\bold{sin \theta = cos \theta}$

$\longrightarrow \: tan \theta = 1$

$\longrightarrow \: tan \theta = \: tan 45 \degree$

$\longrightarrow \boxed {\bold {\mathfrak{ \theta = 45 \degree}}}$

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Answer 2

Given that :-

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${\bold{Sin\theta = Cos\theta}}$

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Now :-

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$\sf :\implies \:{\bold{\dfrac{Sin\theta}{Cos\theta} = 1 }}$

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$\sf{\red{\boxed{\bold{tan\theta = \dfrac{Sin\theta}{cos\theta}}}}}$

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$\sf:\implies \:{\bold{tan\theta = 1 }}$

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From trigonometric value table :-

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$\sf{\red{\boxed{\bold{tan45 = 1 }}}}$

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$\sf :\implies\: {\bold{tan\theta = tan 45}}$

$\sf:\implies\: {\bold{\theta = 45 }}$

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$\sf{\underline{\huge{\boxed{\bold{More\: to \: explore }}}}}$

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$\Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 60^{\circ} & \sf 90^{\circ} \\ \cline{1-6} \sin & 0 & \dfrac{1}{2 } & \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} & 1 \\ \cline{1-6} \cos & 1 & \dfrac{ \sqrt{ 3 }}{2} } & \dfrac{1}{ \sqrt{2} } & \dfrac{ 1 }{ 2 } & 0 \\ \cline{1-6} \tan & 0 & \dfrac{1}{ \sqrt{3} } & 1 & \sqrt{3} & \infty \\ \cline{1-6} \cot & \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } &0 \\ \cline{1 - 6} \sec & 1 & \dfrac{2}{ \sqrt{3}} & \sqrt{2} & 2 & \infty \\ \cline{1-6} \csc & \infty & 2 & \sqrt{2 } & \dfrac{ 2 }{ \sqrt{ 3 } } & 1 \\ \cline{1 - 6}\end{tabular}}$