Question

How do you express `cos( (3 pi)/ 2 ) * cos (( 5 pi) /6 )` without using products of trigonometric functions?

Answer 1

`cos((3pi)/2)*cos((5pi)/6)= color(green)(0)`

Explanation:

`(3pi)/2=-pi/2` and `(5pi)/6=pi-pi/6`
are standard angles.

Using these standard angles:

`color(white)("XXX")cos((3pi)/2)=cos(-pi/2)=cos(pi/2)=0`

So
`color(white)("XXX")cos((3pi)/2)*cos((5pi)/6)=0xxcos((5pi)/6)=0`