Question

How do you simplify `(sintheta - costheta)^2 + (sintheta+costheta)^2`?

Answer 1

2

Explanation:

`(a+b)^2=a^2+2ab+b^2`
`(a-b)^2=a^2-2ab+b^2`
`(a+b)^2+(a-b)^2=2(a^2+b^2)`

so
`(sintheta-costheta)^2+(sintheta+costheta)^2=2(sin^2theta+cos^2theta)=2`