How do you evaluate sin(5π9)cos(7π18)cos(5π9)sin(7π18)?

1 Answer
Apr 16, 2016

12

Explanation:

This equation can be solved using some knowledge about some trigonometric identities. In this case, the expansion of sin(AB) should be known:

sin(AB)=sinAcosBcosAsinB

You'll notice that this looks awfully similar to the equation in the question. Using the knowledge, we can solve it:
sin(5π9)cos(7π18)cos(5π9)sin(7π18)
=sin(5π97π18)
=sin(10π187π18)
=sin(3π18)
=sin(π6), and that has exact value of 12