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Question

The value of tan θ+tan 60°+θ+tan 120°+θ is
(a) 3 tan 3 θ
(b) tan 3 θ
(c) 3 cot 3 θ
(d) cot 3 θ

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Solution

(a) 3 tan 3 θ

tan θ+ tan60°+θ+tan120°+θ=tan θ+tan60°+tanθ1-tan60°tanθ+tan 120°+tan θ1-tan 120° tanθ =tan θ +3+tan θ1-3tanθ+-3+tanθ1+3tanθ =tan θ1-3tan2θ+3+tanθ1+3tanθ+-3+tanθ1-3tanθ1-3tan2θ =tan θ-3tan3θ+3+3tanθ+tanθ+3tan2θ+tanθ-3tan2θ-3+3tanθ1-3tan2θ =9tanθ-3tan3θ1-3tan2θ =33tanθ-tan3θ1-3tan2θ =3tan3θ

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