Question

√2sinx-√2cosx=2

Answer 1

That would be false. It equals -1. If thats what your asking.

Answer 2

I do not know, the teacher asked to solve this equation at home

Answer 3

I would assume she's asking for the solution to that problem, which would be
\[ x= 3\pi / 4 \text{ or } x = 135 \text{ degrees} \]

Answer 4

Or more exactly ;),
\[x=\frac{3\pi}{4}+2\pi k\]
\[k=0,1,\ldots\]

Answer 5

Dividing through by the square root gives you
\[ sin(x) - cos(x) = \sqrt{2} \]
Squaring both sides will give you
\[\sin^2(x) + cos^2(x) - 2\sin(x)\cos(x) = 2 \]
but the first part of that is 1, so that means
\[ 1 - 2\sin(x)\cos(x) = 2 \implies 2\sin(x)\cos(x) =-1\]
Your trigonometry identities should tell you that
\[2 \sin(x)\cos(x) = \sin(2x) \]
So then
\[ \sin(2x) = -1 \]
the sine function is -1 at 3pi /2, so
\[2x = \frac{3\pi}{2} \implies x = \frac{3\pi}{4} \]

Answer 6

Thank you very much!