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\begin { equation } \begin{array}{l}{\text { Prove the following identity: }} \\ {\text { If } \sqrt{3} \cot ^{2} \theta-4 \cot \theta+\sqrt{3}=0, \text { then find }} \\ {\text { value of } \cot ^{2} \theta+\tan ^{2} \theta}\end{array} \end { equation } |
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Answer» Given √3 cot^2θ - 4cotθ +√3 = 0.⇒ √3 Cot^2θ - 3 Cotθ - Cot θ+√3 = 0⇒ √3 Cotθ( Cotθ - √3) - 1( Cot θ - √3) = 0⇒ ( Cotθ - √3)(√3 Cotθ - 1) = 0Cot θ = √3andCot θ = 1 / √3.letCot θ = √3 and Tan θ = 1 / √3.NowCot^2θ +Tan^2θ= 3 + 1 / 3 = 10 / 3. |
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