for this i tried squaring both sides which gave me sin^2 x = 2-1 = 1

which didn't work

then i tried going backwards with the cos equation

cos^2x = (1-sin^2 x) = a + b sqrt2

rearranged to get sin^2x = -a -b sqrt2 + 1

i didnt know what to do from here

please help thanks

YEEEEEET Feb 3, 2019

#1**+1 **

sin x = sqrt (2) - 1

sin^2 x = [ sqrt (2) - 1 ] ^2 = [ sqrt (2) - 1 ] * [ sqrt (2) - 1 ] =

sqrt (2) *sqrt (2) - 1*sqrt(2) - 1*sqrt(2) + (-1)(-1) =

2 - 2sqrt (2) + 1 =

[ 3 - 2sqrt (2) ]

So.....using an identity.....

cos^2x = 1 - sin^2 x

And we have that

1 - [ 3 - 2sqrt(2) ] =

-2 + 2sqrt (2) .....so a = -2 and b = 2

CPhill Feb 3, 2019