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tmua.me Extreme Set B Paper 2 · Q20

Paper 2TrigonometrySequences & series

The four numbers

sin⁡α,cos⁡α,sin⁡β,cos⁡β,\sin\alpha,\qquad\cos\alpha,\qquad\sin\beta,\qquad\cos\beta,

when arranged in increasing order, form an arithmetic progression with positive common difference. The angles α\alpha and β\beta are real, and cos⁡αcos⁡β≠0\cos\alpha\cos\beta\ne0.

What is the sum of all the distinct possible values of

tan⁡αtan⁡β ?\tan\alpha\tan\beta\,?
A11
B109\dfrac{10}{9}
C829\dfrac{82}{9}
D1010
E919\dfrac{91}{9}
F1009\dfrac{100}{9}

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