Quadratic equations + trigonometry

if α,β are two different values of θ lying between 0 and 2Πwhich satisfy the equation 6 cos θ + 8 sin θ = 9,then find the value of sin(α + β).

2 Answers

Sushovan Halder ·

First keep 6cosθ on one side and square the expression to get a quadratic in sinθ.From this evaluate sinα.sinβ.
Nxt keep the 8sinθ on one side and square to get a quadratic in cosθ.Find out cosα.cosβ.Now u can easily find out cos(α+β) and the n find sin(α+β)

Amartya Kumar Mistry ·

well for this you have to be also careful about the sign of the answer, as given θ lies between 0 and 2π

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