Question

Solve for x,y?

`| sinx +cosx|^(sin^2x-frac{1}4)`=1 +`|siny|`
and `cos^2y=1+sin^2y`

Answer 1

.Someone please double check...
see below

Explanation:

Let's try to solve for y in the second equation:
`cos^2y=1+sin^2y`
`(1-sin^2y)=1+sin^2y`
`sin^2y= 0`
`y= 0, pi`
General solution for y:
`y= 0+pin`
Where n is an element of all integers

Solve for x:
Plug in any feasible solution for y:
`|sinx+cosx|^(sin^2x-1/4)= 1+|sin(0)|`
`|sinx+cosx|^(sin^2x-1/4)= 1`
Recalling:
`x^0=1`
`sin^2x-1/4=0`
`sin^2x=1/4`
`sinx= +-1/2`
`x= pi/6, (5pi)/6, (7pi)/6, (11pi)/6`

General solutions for x:
`x= pi/6+pin`
`x= (5pi)/6+pin`
Where n is an element of all integers