tmua.me Extreme Set B Paper 1 · Question 9

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tmua.me Extreme Set B Paper 1 · Q9

Paper 1TrigonometrySequences & seriesAlgebra

For a real constant $k$ , the equation

\sin^3\theta+\cos^3\theta=k

has exactly three distinct solutions $\theta_1,\theta_2,\theta_3$ with $0\leq\theta<2\pi$ .

What is the value of

\sum_{i=1}^{3}\bigl(\sin\theta_i+\cos\theta_i\bigr)^2\,?

3-\sqrt3

4-\sqrt3

3

2\sqrt3

6-2\sqrt3

4

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