Multiple choice

Number of roots of the equation $\displaystyle \sin x+2\sin 2x= 3+\sin 3x$ in $\left [ 0,\pi \right ]$ is/are

  1. 2

  2. 3

  3. 0

  4. 4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using trigonometric identities, the equation sin(x) + 2sin(2x) = 3 + sin(3x) has a maximum value of 1 + 2 + 1 = 4 for the LHS, but the RHS is 3 + sin(3x). Testing values in [0, pi], the equation simplifies to sin(x) + 4sin(x)cos(x) = 3 + 3sin(x) - 4sin^3(x). There are no real solutions in the interval [0, pi].

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