Question

Use a sum or difference formula to find the exact value of

Sin 11pi/12 cos 2pi/3 - cos 11pi/12 sin2pi/3

Answer 1

We obtain sin( 11pi/12 - 2pi/3 ) = sin( 11pi/12 - 8pi/12 ) = sin( 3pi/12) = sin(pi/4) = $\frac{ \sqrt{2} }{2} ;$  (ave the formula sinxcosy - cosxsiny = sin(x-y));