tmua.me Extreme Set C Paper 1 · Question 12

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tmua.me Extreme Set C Paper 1 · Q12

Paper 1TrigonometryGeometry

For each real angle $\theta$ , let $m$ and $M$ be the smallest and largest, respectively, of the four numbers

|\sin\theta|,\qquad |\cos\theta|,\qquad |\sin\theta+\cos\theta|,\qquad |\sin\theta-\cos\theta|.

What is the greatest possible value of $mM$ ?

\dfrac13

\dfrac25

\dfrac35

\dfrac12

\dfrac34

1

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