Question

prove that sin(alpha+30)=cos alpha +sin(alpha-30)​

Answer 1

Answer:

Step-by-step explanation:

sin ( a + 30  ) = cos a + sin ( a - 30 )

RHS

sin ( a - 30  ) + sin  ( 90 -a )

= sin a cos 30 - sin 30 cos a + sin 90 cos a - cos 90 sin a

= sin a √3 / 2 -  1 / 2 cos a + 1 cos a - 0 sin a

= √3 /2 sin a -  1/2 cos a + cos a

= √3 / 2 sin a +  1 / 2 cos a

sin ( a + 30 ) = sin a cos 30 + cos a sin 30

                     = √3 / 2 sin a + 1/2 cos a = RHS