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tmua.me Medium Set A Paper 1 · Q6

Paper 1TrigonometryAlgebra

The equation

2cos⁡2θ=3sin⁡θcos⁡θ2\cos^2\theta=3\sin\theta\cos\theta

has four distinct solutions θ1,θ2,θ3,θ4\theta_1,\theta_2,\theta_3,\theta_4 with 0≤θ<2π0\leq\theta<2\pi. What is the value of

sin⁡2θ1+sin⁡2θ2+sin⁡2θ3+sin⁡2θ4 ?\sin^2\theta_1+\sin^2\theta_2+\sin^2\theta_3+\sin^2\theta_4\,?
A413\dfrac{4}{13}
B813\dfrac{8}{13}
C2113\dfrac{21}{13}
D3413\dfrac{34}{13}
E44

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