CDS 2023 · PYQ · Trigonometry · medium
Which one of the following is a value of θ, if θ satisfies the equation tan 2θ tan 4θ − 1 = 0; 0 < θ < π/2?
Answer
The correct answer is C: π/12. tan2θ·tan4θ = 1 ⟹ tan4θ = cot2θ = tan(π/2−2θ). So 4θ = π/2−2θ + nπ, giving 6θ = π/2, θ = π/12.
- A.π/15
- B.π/6
- C.π/12✓ Correct
- D.π/5
tan2θ·tan4θ = 1 ⟹ tan4θ = cot2θ = tan(π/2−2θ). So 4θ = π/2−2θ + nπ, giving 6θ = π/2, θ = π/12.
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