My question is can the following be factored. I am a teacher who needs the factors to this right away. 2 Sin²X + 2 SinX CosX - 1= 0

Thanks
Diane

Hi Diane

Factors I don't see but if the problem is to solve for x then the double angle expressions for sine and cosine make it possible.

sin 2x = 2 sin x cos x

and

cos 2x = cos²x - sin²x = 1 - 2 sin²x

Thus

2 sin²x + 2 sin x cos x -1 = 0

is equivalent to

sin 2x - cos 2x = 0

which is

sin 2x = cos 2x

or

tan 2x = 1.

Hence, in the first quadrant, 2x is 45^o

Cheers
Harley