Question

Find the general solution of the equation sin3x + sinx =sin2x

Answer 1

◀HERE'S ⏬ YOUR ANSWER▶

$sin3x + sinx = sin2x \\ or \: \: 2sin( \frac{3x +x }{2} ) \: cos( \frac{3 x - x }{2} ) = sin2x \\ or \: \: 2sin2x \: cosx = sin \: 2x \\ or \: \: sin2x(2cosx - 1) = 0 \\ \\ so \: \: sin2x = 0 \\ or \: \: sin2x = sin0 \\ or \: \: x = 0 \\ \\ \\ again \\ 2cosx - 1 = 0 \\ or \: \: cosx = \frac{1}{2} \\ or \: \: cosx = cos60 \\ or \: \: x = 60 \\ \\ hence \: the \: required \: solution \: is \\ x = 0 \: \: or \: \: x = 60$

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