Question

if tan(11x)=tan34 and tan(19x)=tan21 find the value of tan(5x)

Answer 1

Solution :-

we know that, general solution for tan θ = tan ∅ is ,

• θ = nπ + ∅ , where n ∈ Z [ n = 0, ± 1, ± 2, ± 3, ___]

so,

→ tan(11x) = tan(34°)

→ 11x = 34° + nπ ------- Eqn.(1)

and,

→ tan(19x) = tan(21°)

→ 19x = 21° + mπ -------- Eqn.(2)

Multiply Eqn.(1) by 3 and Eqn.(2) by 2 we get,

→ 33x = 102° + 3nπ ------- Eqn.(3)

→ 38x = 42° + 2mπ -------- Eqn.(4)

subtracting Eqn.(3) from Eqn.(4), we get,

→ 38x - 33x = (42° - 102°) + (2mπ - 3nπ)

→ 5x = (-60°) + (2m - 3n)π

therefore,

→ tan(5x) = tan(-60°)

→ tan(5x) = (-√3) (Option 2) (Ans.)

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