Use the sum/difference formula to find the exact answer.

Question

(cos (11π/15) cos (π/10)) - (sin (11π/15) sin (π/10))  

 

(p.s. π = pi)

 

Please don't give a decimal as the answer.  I need the exact answer.

Answer 1

cos(11π/15)cos(π/10) - sin(11π/15)sin(π/10) = cos(11π/15 + π/10)

                          

                                                              = cos(22π/30 + 3π/30)

 

                                                              = cos(25π/30)

 

                                                              = cos(5π/6)

 

                                                              = -√3/2