Solve the equation: 2 sin^2 x = 3 cos x - Maths - Trigonometric Functions

Question

Solve the equation: 2 sin^2 x = 3 cos x

Aman Rajput · Accepted Answer

Dear Student

2sin2x=3cos x⇒2-2cos2x-3cos x = 0⇒2 cos2x + 3 cos x - 2 = 0⇒2 cos2x + 4 cos x - cos x - 2 = 0⇒2 cos xcos x + 2 - 1cos x + 2 = 0⇒(2cosx-1)(cosx+2)=0⇒2 cos x - 1 = 0  or  cos x + 2 = 0⇒cos x =12  or  cos x = -2  rejected⇒cos x=cosπ3⇒x=2nπ±π3 , n∈Z
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