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tmua.me Extreme Set A Paper 1 · Q12

Paper 1Trigonometry

The angles α\alpha and β\beta satisfy

0<α<π2,0<β<π2,tan⁡α+tan⁡β=2.0<\alpha<\frac\pi2,\qquad 0<\beta<\frac\pi2, \qquad \tan\alpha+\tan\beta=\sqrt2.

What is the least possible value of

sin⁡2α+sin⁡2β ?\sin^2\alpha+\sin^2\beta\,?
A3−32\dfrac{3-\sqrt3}{2}
B2−32-\sqrt3
C13\dfrac13
D23\dfrac23
E3−1\sqrt3-1
FThere is no least value\text{There is no least value}

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