Question

2 Sin A Cos B equals?​

Answer 1

Answer:

2 cosA sinB = sin(A + B) − sin(A − B) 2 cosA cosB = cos(A + B) + cos(A − B) 2 sinA sinB = cos(A − B) − cos(A + B)

l hope you understand.....

Answer 2

Given:

2 Sin A Cos B equals?​

Solution:

Know that,

$\[sin\left( {A + B} \right) = sin{\rm{ }}AcosB + cosAsinB\]$         ------(1)

$\[sin\left( {A - B} \right) = sinAcosB - cosAsinB\]$       ------(2)

Add equation (1) and equation (2)

$\[\begin{array}{l} \Rightarrow sin\left( {A + B} \right) + sin\left( {A - B} \right) = sin{\rm{ }}AcosB + sin{\rm{ }}AcosB\\ \Rightarrow sin\left( {A + B} \right) + sin\left( {A - B} \right) = 2sin{\rm{ }}AcosB\\ \Rightarrow 2sin{\rm{ }}AcosB = sin\left( {A + B} \right) + sin\left( {A - B} \right)\end{array}\]$

Hence, $\[2sin{\rm{ }}AcosB\]$ is equals to the $\[sin\left( {A + B} \right) + sin\left( {A - B} \right)\]$.