Question

If A = 60⁰ and B = 30⁰, verify that: 
(i) sin (A + B) = sin A cos B + cos A sin B

Answer 1

A = 60⁰ and B = 30⁰ 
Now, A + B = 60⁰ + 30⁰ = 90⁰ 
Also, A – B = 60⁰ – 30⁰ = 30⁰  
(i) sin (A + B) = sin 90⁰ = 1 
sin A cos B + cos A sin B = sin 60⁰ cos 30⁰ + cos 60⁰ sin 30⁰ 

=`(sqrt(3)/2xx sqrt(3)/2 + 1/2xx1/2) = (3/4+1/4)=1`

∴ sin (A + B) = sin A cos B + cos A sin B