Trigonometric EquationHard
Question
If tan θ + tan4θ + tan7θ = tan θ tan4θ tan7θ, then θ =
Options
A.
B.
C.
D.nπ
Solution
tan θ + tan 4θ + tan 7θ = tan θ tan 4θ tan 7θ
tan θ + tan 4θ = - tan 7θ [1 - tan θ tan 4θ]
= tan (-7θ)
⇒ 5θ = nπ - 7θ
12θ = nπ ⇒ θ =
tan θ + tan 4θ = - tan 7θ [1 - tan θ tan 4θ]
= tan (-7θ)⇒ 5θ = nπ - 7θ
12θ = nπ ⇒ θ =
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