Step-by-step explanation:
[tex] \frac{ \sin(3A) + \sin(A) }{2 \sin(2A) } [/tex]
Using the trigonometric identity
[tex] \sin(x) + \sin(y) = 2 \sin( \frac{x + y}{2} ) \cos( \frac{x - y}{2} ) [/tex]
Rewrite the expression
We have
[tex] \frac{2 \sin(2A) \cos(A) }{2 \sin(2A) } [/tex]
Reduce the fraction with 2
That's
[tex] \frac{ \sin(2A) \cos(A) }{ \sin(2A) } [/tex]
Reduce the fraction with sin 2A
We have the final answer as
cos A
As proven
Hope this helps you
