Question:
\sqrt(2)(sinx+cosx)=\sqrt(3)
Answer:
√2 * (sin x + cos x) = √3
=> √2/2 * (sin x + cos x) = √3/2 [Divide by 2 on both sides]
=> 1/√2 * (sin x + cos x) = √3/2
=> sin x * 1/√2 + cos x * 1/√2 = √3/2
=> sin x * cos π/4 + cos x * sin π/4 = √3/2
=> sin (x + π/4) = sin π/3 [Apply sin(A + B) formula]
=> x + π/4 = nπ + (-1)n * π/3
=> x = nπ + (-1)n * π/3 - π/4
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