Question

How do you simplify using the double angle formula `1-2sin^2(-75)`?

Answer 1

See explanation.

Explanation:

`1-2sin^2(-75)=`
`sin^2(-75)+cos^2(-75)-2sin^2(-75)=` (1)
`cos^2(-75)-sin^2(-75)=`
`cos(2*(-75))=` (2)
`cos(-150)=cos(150)=` (3)
`cos(180-30)=-cos(30)=-sqrt(3)/2` (4)

During calculations I used the following identities:

1. `sin^2x+cos^2x=1`
2. `cos2x=cos^2x-sin^2x`
3. `cos(-x)=cos(x)`
4. `cos(180-x)=-cos(x)`