Solving Quandratic Trigonometric Equations

How would I solve these equations?

1) (2sinx - 1)cosx = 1

2) (2 cosx + √3)sinx = 0

I tried to convert them to the same identity, but wasn't able to find a substitute in neither the pythagorean identities or the double angle formulas, and I'm lost as to what to do now. Any suggestions/advice would be appreciated, thanks in advance!

Re: Solving Quandratic Trigonometric Equations

Hello, misiaizeska!

The second one is easy . . . the product is zero.

We have:

. .

. .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

I have an incomplete solution for the first one.

We have: .

Square both sides: . . . . . . .

. . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

n . . . . . . . .

. .

I found one root: .

I don't know if there are any others . . .

Re: Solving Quandratic Trigonometric Equations

Thank you very much, that was really helpful and I was able to figure it out!