How do you express cos(3π2)cos(3π4) without using products of trigonometric functions?

1 Answer
May 3, 2016

cos(3π2)cos(3π4)=0

Explanation:

As cos(AB)=cosAcosBsinAsinB and cos(A+B)=cosAcosB+sinAsinB, adding them

2cosAcosB=cos(A+B)+cos(AB)

or cosAcosB=12×cos(A+B)+12×cos(AB)

Hence cos(3π2)cos(3π4)

= 12×cos((3π2)+(3π4))+12×cos((3π2)(3π4))

= 12{cos(9π4)+cos(3π4)}

= 12{cos(2π+π4)+cos(ππ4)}

= 12{cos(π4)cos(π4)}=0