Aptitude question for Accenture

Ques. If v3 cot^2? - 4cot?+ v3 =0, then find the value of cot^2? + tan^2?

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  • Sol:
    Given √3 cot2θ - 4cotθ + √3 = 0.

    ⇒ √3 Cot2θ - 3 Cot θ - Cot θ+ √3 = 0

    ⇒ √3 Cot θ( Cot θ  - √3)  - 1( Cot θ - √3)  = 0

    ⇒ ( Cot θ  - √3)(√3 Cot θ - 1) = 0

    Cot θ = √3  and  Cot θ = 1 / √3 .

    let Cot θ = √3 and Tan θ = 1 / √3 .

    Now Cot2θ +Tan2θ = 3 + 1 / 3 = 10 / 3.
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  • Given √3 cot2θ - 4cotθ + √3 = 0.

    ⇒ √3 Cot2θ - 3 Cot θ - Cot θ+ √3 = 0

    ⇒ √3 Cot θ( Cot θ  - √3)  - 1( Cot θ - √3)  = 0

    ⇒ ( Cot θ  - √3)(√3 Cot θ - 1) = 0

    Cot θ = √3  and  Cot θ = 1 / √3 .

    let Cot θ = √3 and Tan θ = 1 / √3 .

    Now Cot2θ +Tan2θ = 3 + 1 / 3 = 10 / 3.
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