Question

How do you find the exact value of `cos ((2pi)/9) cos (pi/18)+sin ((2pi)/9) sin (pi/18)`?

Answer 1

`sqrt3/2`

Explanation:

This is of the form `cos(a-b)=cos (a)cos (b)+sin (a)sin (b)`

The above expression simplifies to

`cos (2pi/9 - pi/18)`
`cos (3pi/18)`

`cos (pi /6) = cos 30 = sqrt3/2`

Answer 2

`color (red)(sqrt3/2)`

Explanation:

we know that
`color (cyan)(cos (A-B)=cosA×cosB+sinA×sinB)`
similarly the equation given is question can be written as
`cos (2pi/9-pi/18)`
`cos ((4pi-pi)/18)`
`cos (3pi/18)`
`cos (pi/6)`
`cos ((180°)/6)`
`color (green)(cos (30°) = sqrt3/2)`