Question

Simplify 1+sin²x/2=?
how can i simplify it into cos x form?

Answer 1

`(1)/(2)` ( 3 - cosx)

using the double angle formula

cos2x = 1 - 2sin²x

then cosx = 1 - 2sin²(
`(x)/(2)`)

⇒ sin² (
`(x)/(2)`) = -
`(1)/(2)` ( cosx - 1 )

⇒ 1 + sin²(
`(x)/(2)`)

= 1 -
`(1)/(2)`( cosx - 1 )

= 1 -
`(1)/(2)`cosx +
`(1)/(2)`

=
`(3)/(2)` -
`(1)/(2)`cosx

=
`(1)/(2)`( 3 - cosx )