Maharashtra State BoardHSC Science (General) 11th
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Prove the following: tan8θ − tan5θ − tan3θ = tan8θ tan5θ tan3θ - Mathematics and Statistics

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Sum

Prove the following:

tan8θ − tan5θ − tan3θ = tan8θ tan5θ tan3θ

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Solution

∵  8θ = 5θ + 3θ

∴ tan8θ = tan(5θ + 3θ)

∴ tan8θ = `(tan5theta + tan3theta)/(1 - tan5theta . tan3theta)`

∴ tan8θ (1 − tan5θ . tan3θ) = tan5θ + tan3θ

∴ tan 80 – tan 8θ · tan 5θ · tan 3θ = tan 5θ + tan 3θ

∴ tan 8θ – tan 5θ – tan 3θ = tan 8θ · tan 5θ · tan 30

Concept: Trigonometric Functions of Multiple Angles
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