Trigonometric EquationHard

Question

αis solution of equation 49^cosx - 13.(7)^cosx + 40 = 0 in [0, 2π], then -

Options

A.number of possible values of α is 4.

B.number of possible values of α is 2.

C.sum of all values of α is 4π

D.sum of all values of α is 2π

Solution

7^cosx = t
t² - 13t + 40 = 0
⇒ t = 8 or 5
⇒ cosx = log₇8 (rejected) or cos α = log₇5
α₁ + α₂ = 2π

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