Question

Solve the equation.
cos 3x = sin 2x

Answer 1

We know that principal value branch of

${sin}^{ - 1} x = [-\frac{\pi}{2} \frac{\pi}{2}]$

here in the equation we had either convert cos 3x into sin

as we know that

$sin \: x = cos \: (90 - x)$

To solve the given equation we must keep consider that sin and sin inverse cancels each other only if x belongs to its principal value .

$cos \: 3x = sin \: 2x \\ \\ sin \: (90 - 3x) = sin \: 2x$

taking sin inverse both sides

$(90 - 3x) = \: 2x \\ \\ 2x + 3x = 90 \\ \\ 5x = 90 \\ \\ x = \frac{90}{5} \\ \\ x = 18$

is the solution of the equation.