Question

How do you find the exact value of `cos(120^circ+45^circ)`?

Answer 1

`cos(120^@+45^@)=(-1-sqrt3)/(2sqrt2)=(-sqrt2-sqrt6)/4`

Explanation:

As `cos(A+B)=cosAcosB-sinAsinB`

`cos(120^@+45^@)`

= `cos120^@cos45^@-sin120^@sin45^@`

= `(-1/2)*1/sqrt2-sqrt3/2*1/sqrt2`

= `(-1-sqrt3)/(2sqrt2)`

or `(-1-sqrt3)/(2sqrt2)*sqrt2/sqrt2=(-sqrt2-sqrt6)/4`