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    Question

    What is the value of [(tan 5θ + tan 3θ)/4 cos 4θ (tan 5θ – tan 3θ)]?

    A sin 2θ Correct Answer Incorrect Answer
    B cos 2θ Correct Answer Incorrect Answer
    C tan 4θ Correct Answer Incorrect Answer
    D cot 2θ Correct Answer Incorrect Answer

    Solution

    tan(5 θ + tan3 θ) cos4 θ (tan(5 θ   - 3 θ )) / 4 Put θ = 150, 5 θ = 750 tan 750 + tan 450 / 4 × cos 600 tan (5 θ – 3 θ) tan750 = √3 + 1 / √3 – 1                 = 1 + 3 + 2√3 / 2                 = 2 +√3 = 2 + √3 + 1 / 4 × ½ (2 + √3 – 1) = 3 +√3 / 2√3 + 1 = √3(1 +√3) / 2 (1 + √3) = √3 / 2 Cos2 θ Cos2 × 150 Cos 300 = √3 / 2

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