Question

How do you use the sum or difference identity to find the excat value of sin 165°​

Answer 1

`(1)/(4)` (
`√(6)` -
`√(2)` )

Explanation:

Using the addition formula for sine

sin(A + B) = sinAcosB + cosAsinB

Given

sin165° = sin(120 + 45)° , then

sin(120 + 45)°

= sin120°cos45° + cos120°sin45°

= sin60°cos45° - cos60°sin45°

=
`(√(3) )/(2)` ×
`(√(2) )/(2)` -
`(1)/(2)` ×
`(√(2) )/(2)`

=
`(√(6) )/(4)` -
`(√(2) )/(4)`

=
`(1)/(4)` (
`√(6)` -
`√(2)` )