How to Verify that sin(A+B) + sin(A-B) = 2sinA cosB ?

Question

8494 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-14T19:08:54

Use #sin(A + B) = sinAcosB + sinBcosA# and #sin(A - B) = sinAcosB - sinBcosA#.

#sinAcosB + sinBcosA + sinAcosB - sinBcosA = 2sinAsinB#

#2sinAcosB = 2sinAcosB#

Hopefully this helps!

Answer 2 · 2018-04-14T19:18:36

Please see below.

We know that,

#color(red)((1)sin(A+B)=sinAcosB+cosAsinB#

#color(red)((2)sin(A-B)=sinAcosB-cosAsinB#

Here,

#sin(A+B) + sin(A-B) = 2sinA cosB #

Using #(1) and(2)#

#LHS=(A+B) + sin(A-B) #

#=sinAcosB+cancel(cosAsinB)+sinAcosB-cancel(cosAsinB)#

#=2sinAcosB#

#=RHS#

But ,if #RHS=2sinAsinB#, then it is clear that

#LHS!=RHS#