Question

Anybody know the answer?

Answer 1

we are given

`1-2sin^2((x)/(2) )`

we can use trigonometric identity

we know that

`sin^2((x)/(2) )+cos^2((x)/(2) )=1`

now, we can replace 1 as this

`=sin^2((x)/(2) )+cos^2((x)/(2) )-2sin^2((x)/(2) )`

now, we can simplify it

and we get

`=cos^2((x)/(2) )-sin^2((x)/(2) )`

now, we can use half angle formula

`cos(\theta)=cos^2((\theta)/(2) )-sin^2((\theta)/(2) )`

so, we will get

`cos^2((x)/(2) )-sin^2((x)/(2) )=cos(2*(x)/(2))`

`=cos(x)`

so,

`1-2sin^2((x)/(2) )=cos(x)`.............Answer