Question

equation in interval [0,2pi) 10. sin 2x + cos x = 0

Answer 1

Well,
sin 2x = 2 sin x . cos x

See what to do now?

Answer 2

No?
Well this means that
sin 2x + cos x = 0

is equivalent to
2.sin x.cos x + cos x = 0

cos x (2sin x + 1) = 0

Now see what to do?

Answer 3

The problem looks for pi something

Answer 4

Intervals such as 0,2pi

Answer 5

If ab = 0, what can you say about a and b?
If ab = 0, then
a = 0 or b = 0

Likewise if
cos x (2sin x + 1) = 0

then
cos x = 0 or 2sin x + 1 = 0

Now solve for x, given that x is in the interval [0, 2pi)

Answer 6

I don't how

Answer 7

Well if
cos x = 0,
what must x be if x is in [0, 2pi) ?

Answer 8

I don't understand