Safwan A.

# Solve: sin2x-sin4x+sin6x=0

This question is from trigonometry chapter in mathematics of class 11th.
"Cbse board"

## 2 Answers By Expert Tutors

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Tutor
4.9 (42)

Effective Mathematics Tutor

Paul M.

tutor
OK, now I can give you the whole thing...at least I will tell you how to do it.
First, graph the equation so that you see that it is periodic with period π.
Make the substitution sin 6x = sin 4x cos 2x + cos 4x sin 2x  and collect terms.
Next make the substitution sin 4x = 2 sin x cos x and factor out sin 2x which means sin 2x gives you some roots.
Collect terms and make the substitution sin2x = 1 - cos2x and collect terms again.
You should now have 4 cos2 2x - 2 cos 2x. Divide out the 2.
Factor out the cos 2x which means cox 2x = 0 gives you some more roots.
You should now be left with 2 cos 2x - 1 = 0, i.e. cos 2x = 1/2 which will give you the rest of the roots.
Good luck.
If you have a graphing calculator which will allow you to graph multiple equations at once & if you graph the original equation along with the 3 root equations, you will see that you get all the roots.

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09/05/18

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