Question

How do you simplify `1-2sin^2( theta/3)` by using a double-angle formula?

Answer 1

`cos((2theta)/3)`

Explanation:

Using the appropriate `color(blue)"double angle formula"`

`color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(cos2theta=cos^2theta-sin^2theta)color(white)(a/a)|)))`

also `color(red)(|bar(ul(color(white)(a/a)color(black)(sin^2theta+cos^2theta=1rArrcos^2theta=1-sin^2theta)color(white)(a/a)|)))`

`rArrcos2theta=cos^2theta-sin^2theta=(1-sin^2theta)-sin^2theta`

`rArrcos2theta=1-2sin^2theta`

`rArr1-2sin^2(theta/3)=cos((2theta)/3)`