How do you express cos(15π8)cos(5π3) without using products of trigonometric functions?

1 Answer
Mar 13, 2016

12cos(11π24)+12cos(5π24)

Explanation:

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

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

Hence cosAcosB=12{cos(A+B)+cos(AB)} and

cos(15π8)cos(5π3)=12{cos(15π8+5π3)+cos(15π85π3)}

= 12{cos(45π+40π24)+cos(45π40π24)}

= 12{cos(85π24)+cos(5π24)}

= 12{cos(96π11π24)+cos(5π24)}

= 12{cos(4π11π24)+cos(5π24)}

= 12cos(11π24)+12cos(5π24)}