If e cos 2 x + cos 4 x + cos 6 x + . . . . ∞ log e 2 satisfies the equation t 2 - 9 t + 8 = 0 , then the value of 2 sin x sin x + 3 cos x , where 0 x π 2 , is equal to

Question

If e cos 2 x + cos 4 x + cos 6 x + . . . . ∞ log e 2 satisfies the equation t 2 - 9 t + 8 = 0 , then the value of 2 sin x sin x + 3 cos x , where 0 x π 2 , is equal to, 3 2, 1 2, 3, 2 3

MARKS App · Accepted Answer

e cos 2 x + cos 4 x + … … ∞ ln 2 = 2 cos 2 x + cos 4 x + … … ∞ = = 2 cos 2 x 1 - cos 2 x = 2 cot 2 x t 2 - 9 t + 8 = 0 ⇒ t = 1 , 8 ⇒ 2 cot 2 x = 1 , 8 ⇒ cot 2 x = 0 , 3 0 x π 2 ⇒ cot x = 3 ⇒ 2 sin x sin x + 3 cos x = 2 1 + 3 cot x = 2 4 = 1 2

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