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√3 Cos x + 1 * sinx = √2

divide the equation by 2

√3/2 cos x + 1/2 * Sin x = √2/2

Cos π/6 cos x + sin π/6 Sin x = 1/√2

cos (x -π/6) = cos π/4

x - π / 6 = 2 n π +- π/4

=> x = 2 n π + 5π/12 or 2 n π - π/12

divide the equation by 2

√3/2 cos x + 1/2 * Sin x = √2/2

Cos π/6 cos x + sin π/6 Sin x = 1/√2

cos (x -π/6) = cos π/4

x - π / 6 = 2 n π +- π/4

=> x = 2 n π + 5π/12 or 2 n π - π/12