Question

sin (m+n) A+ sin(m-n)a= 2 sin ma cos na​

Answer 1

Answer:

remember sin(ma + na)= sinmacosna+sinnacosma

and sin(ma - na)= sinmacosna-sinnacosma

Answer 2

Step-by-step explanation:

To Prove :-

sin(M + N) + sin(M - N) = 2sinMcosN

How To Do :-

Here they asked us to Prove 'sin(M + N) + sin(M - N) = 2sinMcosN'. So here we need to take L.H.S(Left Hand side). Here L.H.S is 'sin(M+N) + sin(M - N)'. So we can observe that they are in the form of 'sin(A+B) and sin(A-B)'. So we need to apply that formula of sin(A+B) and sin(A-B). After obtaining that we need to add them.

Formula Required :-

1) sin(A + B) = sinAcosB + cosAsinB

2) sin(A - B) = sinAcosB - cosAsinB

Solution :-

Taking L.H.S :-

= sin(M + N) + sin(M - N)

= (sinM.cosN + cosM.sinN) + (sinM.cosN - cosM.sinN)

Removing brackets :-

= sinMcosN + cosMsinN + sinMcosN - cosMsinN

Cancelling the terms :-

= sinMcosN + sinMcosN

= 2sinMcosN

= R.H.S

Hence proved that 'sin(M + N) + sin(M - N) = 2sinMcosN'.