Question

.If cotθ = 2, then the value of the expression then find the value of Cot^2 θ+cosec^2 θ

Answer 1

Step-by-step explanation:

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Answer 2

SoluTion :-

$\sf\implies cot\theta = 2$

$\sf{\bold{{\underline{\underline{cosec^2\theta - cot^2\theta = 1 }}}}}$

$\sf{\bold{{\underline{\underline{cosec^2\theta = cot^2\theta + 1 }}}}}$

$\sf\implies cot^2\theta + cosec^2\theta$

$\sf\implies cot^2\theta + cot^2\theta + 1$

$\sf\implies 2^2 + 2^2+ 1$

$\sf\implies 4 + 4 + 1$

$\sf\implies 9$

$\sf{\bold{\blue{\underline{\underline{cot^2\theta + cosec^2\theta = 9 }}}}}$

$\sf{\bold{\green{\underline{\underline{Extra\:\:Information}}}}}$

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