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tmua.me Medium Set E Paper 2 · Q16

Paper 2TrigonometryAlgebra

For which real values of kk does the equation

sin⁡θ+cos⁡θ+∣sin⁡θ−cos⁡θ∣=k\sin\theta+\cos\theta+|\sin\theta-\cos\theta|=k

have exactly two distinct solutions satisfying 0≤θ<2π0\leq\theta<2\pi?

A−2<k<2-\sqrt2<k<\sqrt2
B−2≤k<2ork=2-\sqrt2\leq k<\sqrt2\quad\text{or}\quad k=2
C−2<k≤2ork=2-\sqrt2<k\leq\sqrt2\quad\text{or}\quad k=2
D−2<k<2ork=2-\sqrt2<k<\sqrt2\quad\text{or}\quad k=2
E2<k<2\sqrt2<k<2

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