Question

10.cos(A+B) + sin(A - B)=2 sin(45° + A) cos(45° + B)​

Answer 1

Given Cos(A + B) + sin(A - B) = 2sin(45° + A)cos(45° + B)
lift hand side ( LHS )
Cos(A + B) + sin(A - B)
cosAcosB - sinAsinB + sinAcosB - cosAsinB

RHS
=> 2(sin45°cosA + cos45°sinA)(cos45cosB - sin45sinB)

=>2(√2/2cosA + √2/2sinA)(√2/2cosB - √2/2sinB)

=> 2( (1/2)cosAcosB - (1/2)cosAsinB + (1/2)sinAcosB - (1/2)sinAsinB)

=> cosAcosB - cosAsinB + sinAcosB - sinAsinB

LHS = RHS  

HOPE IT'S HELP

Answer 2

Step-by-step explanation:

cos(A+B)+sin(A+B).................................