Question

please help me with the question​

Answer 1

Answer:

x= 0°

or

x= 30°

Step-by-step explanation:

To solve

$sin \: 2x - sin \: 4x + sin \: 6x = 0$

we know that

$sin \: c - sin \: d = 2sin \: (\frac{c + d}{2} ) \times cos( \frac{c - d}{2} ) \\ \\ sin \: 2x + sin \: 6x- sin \: 4x = 0\\ sin \: 2x + sin \: 6x = 2sin \: (\frac{2x + 6x}{2} ) \times cos( \frac{2x - 6x}{2} ) \\ \\ = 2sin \: 4x \: cos( - 2x) \\ \\ so \: \\ \\ 2sin \: 4x \: cos \: 2x- sin \: 4x = 0 \\ \\ sin \: 4x \: .(2cos2x - 1) = 0 \\ \\ sin \: 4x = 0 \\ \\ 4x = 0 \\ \\ x = 0 \\ \\ 2 \: cos \: 2x - 1 = 0 \\ \\ 2 \: cos \: 2x = 1 \\ \\ \: cos \: 2x = \frac{1}{2} \\ \\ \: cos \: 2x = cos \: 60 \\ \\ 2x = 60 \\ \\ x = 30$

Hope it helps you.