Question

The real roots of the equation `cos^7x+sin^4x=1` in the interval `(-pi,pi)` are __________, ________, and ________

Answer 1

`cos^7x+sin^4x=1`
`cos^7x=1-sin^4x`
`cos^7x=1-(sinx)^2`
`cos^7x=(1-sin^2x)(1+sin^2x)`
`cos^7x-cos^2x(1+sinn^2x)=0`
`cos^2x[cos^5x-1-sin^2x]=0`
`cosx=0`
`x=-pi/2,pi/2,0`.