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