Question

take a = 90 and b= 45 to verify that: sin(a-b)=sinacosb-cosasinb,cos(a-b)=cosa cosb + sina sinb

Answer 1

Answer:

sin (90-45) =sin 90 cos 45 - cos 90 sin45

sin 45 = sin 90 cos 45 - cos 90 sin45

Now sin 90 =1 cos 90=0

sin 45 =1/√2 cos 45=1/√2

put the values in equation and you get-

1/√2 = 1 ×1/√2 - 0×1/√2

1/√2=1/√2

You can prove also prove cos (a-b) the same way

Hope it was helpful!