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Euclid Sample Paper 1 · Q12

Paper 1Trigonometry

For real θ\theta, define

T=sin⁡θ+cos⁡θ+2sin⁡θcos⁡θ.T=\sin\theta+\cos\theta+2\sin\theta\cos\theta.

Let MM be the maximum possible value of TT, and let mm be the minimum possible value of TT. What is M−mM-m?

A2+22+\sqrt2
B94+2\frac94+\sqrt2
C52+2\frac52+\sqrt2
D1+221+2\sqrt2
E74+22\frac74+2\sqrt2
F33

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