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tmua.me Extreme Set C Paper 2 · Q14

Paper 2Trigonometry

Let θ1,…,θm\theta_1,\ldots,\theta_m be all the distinct real solutions with 0≤θ<2π0\leq\theta<2\pi of

sin⁡ ⁣(π2(2sin⁡θ+cos⁡θ))=cos⁡ ⁣(π2(sin⁡θ−2cos⁡θ)).\sin\!\left(\frac\pi2(2\sin\theta+\cos\theta)\right) = \cos\!\left(\frac\pi2(\sin\theta-2\cos\theta)\right).

What is the value of

sin⁡θ1+⋯+sin⁡θm ?\sin\theta_1+\cdots+\sin\theta_m\,?
A−45-\dfrac45
B00
C−25-\dfrac25
D−65-\dfrac65
E−85-\dfrac85
F45\dfrac45

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