The number of values of x lying in the interval - 2 π , 2 π satisfying the equation 1 + cos ⁡ 10 x cos ⁡ 6 x = 2 c o s 2 8 x + s i n 2 8 x is equal to

Question

The number of values of x lying in the interval - 2 π , 2 π satisfying the equation 1 + cos ⁡ 10 x cos ⁡ 6 x = 2 c o s 2 8 x + s i n 2 8 x is equal to,

MARKS App · Accepted Answer

We have 1 + cos ⁡ 10 x cos ⁡ 6 x = 2 c o s 2 8 x + s i n 2 8 x = c o s 2 8 x + 1 So, cos ⁡ 10 x cos ⁡ 6 x = c o s 2 8 x = 1 + cos ⁡ 16 x 2 ⇒ cos ⁡ 16 x + cos ⁡ 4 x = 1 + cos ⁡ 16 x ⇒ cos ⁡ 4 x = 1 ⇒ 4 x = 2 n π , n ∈ Z ⇒ x = n π 2 , n ∈ Z in - 2 π , 2 π , x = ± 3 π 2 , ± π , ± π 2 , 0 So, the number of values of x is 7 .

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