# Find the General Solution of the Following Equation: Sin 2 X = Cos 3 X - Mathematics

Sum

Find the general solution of the following equation:

$\sin 2x = \cos 3x$

#### Solution

We have:

$\sin2x = \cos3x$
$\cos3x = \sin2x$

⇒ $\cos3x = \cos \left( \frac{\pi}{2} - 2x \right)$

⇒ $3x = 2n\pi \pm \left( \frac{\pi}{2} - 2x \right), n \in Z$

On taking positive sign, we have:
$3x = 2n\pi + \left( \frac{\pi}{2} - 2x \right)$

⇒ $5x = 2n\pi + \frac{\pi}{2}$

⇒ $x = \frac{2n\pi}{5} + \frac{\pi}{10}$

⇒ $x = (4n + 1)\frac{\pi}{10}$

$n \in Z$

Now, on taking negative sign, we have:

$3x = 2n\pi - \frac{\pi}{2} + 2x, n \in Z$
⇒ $x = 2n\pi - \frac{\pi}{2}$
⇒ $x = (4n - 1)\frac{\pi}{2}, n \in Z$
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 11 Trigonometric equations
Exercise 11.1 | Q 2.04 | Page 21