Rewrite 2cos 75°sin 75° using a double-angle identity.

Question

Rewrite 2cos 75°sin 75° using a double-angle identity.

Answer 1

2 cos 75° . Sin 75° = Sin 150°

 

 Notice:

 

  Sin 150 º = Sin 30°

 

  See that    Sin 75° = Cos 15°

 

                   Cos 75° = Sin 15°

 

        So :

                   2Cos 75° . Sin 75° = 2 Sin 15°Cos°15 = Sin 30°