Question

sinx+siny=1/3,answer siny-cos2x

Answer 1

Is that sin(y) - cos(2x) or sin(y) - cos^2(x) ?

Answer 2

yes

Answer 3

Which one. The first one, or the second one. "Yes" is not an answer!

Answer 4

i am sorry ,it is the first one

Answer 5

can you answer this question

Answer 6

Ok, now \[\cos (2x) = \cos^2 x - \sin^2 x = 1 - 2 \sin^2 x\]
So\[\sin y - \cos(2x) = \sin y -1 + 2 \sin^2 x\]

Answer 7

Now you can express sin x in terms of sin y. Substitute that expression into the last equation above and you'll have a quadratic equation in sin y

Answer 8

assume that sin(y)-cos(2x)=z
then sin(y) =z+cos(2x)=z+1-2sin^2(x)
substitute in the first expression
sin(x)+z+1-2sin^2(x)=1/3
sin^2(x)-.5sin(x)-(z+1)/2)=-1/6
(sin(x)-.25)^2-(z+1)/2=1/3
her (sin(x)-.25)^2 is in range L= [0:1.562]
so L=(z+1)/2+1/3
L=z/2+5/6
z=2L-5/3
so z is in range [-1.6666:1.45833]
z is not a number it is a set of number depends on the value of x

Answer 9

That's wrong.