Question

Solve for x: sinx-cosx=√2

Answer 1

use the complementary angle method
Rsinxcosa - Rcosxsina = Rsin(x-a)
compare this with
sinx - cos x = sqrt2
R cosa = 1
R sina = 1

so Rsina / Rcosa = tan a = 1
a = 45 degrees

now you can find value of R

and using Rsin(x - 45) = sqrt2
find x

Answer 2

oh - how to find R
squaring R^2(cos^a + sin^a) = 2
R^2 = 2 and R = sqrt2

Answer 3

sinx - cosx =sqrt(2)
sin^2(x) -2cos(x)sin(x) + cos^2(x) = 2
sin^2(x)+cos^2(x) -2cos(x)sin(x)=2
1-2sinxcosx=2
-2sinxcosx=1
-2(0.5(sin(x+x)+sin(x-x))=1 using identities
-sin2x+sin0=1
sin2x=-1
2x=-90 degrees + k360
x=-45 degrees + k180
or 2x=270 degrees +k360
x= 135 degrees + k180 where k is integer

Answer 4

wow :d

Answer 5

you could leave out -2(0.5(sin(x+x)+sin(x-x))=1 - that is an unnecessary step i did :)
because sin2x=2sinxcosx is quite obvious already