Question

proved that. please tell me answer fast​

Answer 1

Answer:

Step-by-step explanation:

sin(20)sin(40) = (1/2)[cos(20) - cos(60)]  

                      =sin(20)sin(40)sin(80)  

                      = (1/2)[cos(20) - cos(60)]sin(80)  

                      = (1/2)[cos(20)sin(80) - cos(60)sin(80)]  

                      = (1/2)[(1/2)(sin(100)+sin(60)) - (1/2)(sin(140)+sin(20))]  

                      = (1/4)[sin(80) + sin(60) - sin(40) - sin(20)]  

                      = (1/4)sin(60), since sin(80) - sin(40) - sin(20) = sin(60+20) -                              sin(60-20) - sin(20) = 2cos(60)sin(20) - sin(20) = 0  

                      = √3/8