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tmua.co.uk TMUA Mock Paper 1 · Q12

Paper 1TrigonometryFunctions & graphsAlgebra

Consider the equation:

4sin⁡xcos⁡x+22cos⁡x=k(2sin⁡x+2).4\sin x\cos x+2\sqrt2\cos x=k(2\sin x+\sqrt2).

Find the sum of the squares of all possible real values for the constant kk such that the equation has exactly three distinct solutions for xx in the range 0≤x<2π0\le x<2\pi.

A33
B44
C66
D88
E1010
F1212

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