Question

Cos(x)=sin(x). Then the value of cos^4x + sin^4x=?

Answer 1

`1/2`

Explanation:

`Cos(x)=sin(x)`

Usually I avoid dividing by `sinx` or `cosx` because I lose solutions, but we will try solving the equation both ways to see if we get the same solution and all solutions are included:
Divide by `sinx` on both sides:
`cotx=1`
`x=pi/4, (5pi)/4`
`x=pi/4+pin`

Divide by `cosx` on both sides:
`tanx=1`
`x=pi/4, (5pi)/4`
`x=pi/4+pin`

Yields the same solution either way so:
`(+-sqrt2/2)^4 + (+-sqrt2/2)^4=`

`1/4+1/4=1/2`