Answer:
The given equation is never possible i.e cos ( A - B ) ≠ cos A - cos B
Step-by-step explanation:
Given as :
Is cos ( A - B ) = cos A - cos B
To check this possibility , Let us put the value of angle A and B on both side of equation
Now, Let A = 60° and B = 30°
From Left hand side equation
cos ( A - B ) = cos ( 60° - 30° )
Or, cos ( A - B ) = cos 30°
∴ cos ( A - B ) = [tex]\frac{\sqrt{3} }{2}[/tex]
or, cos ( A - B ) = 0.866
From Right hand side equation
cos A - cos B = cos 60° - cos 30°
Or, cos A - cos B = [tex]\frac{1}{2}[/tex] - [tex]\frac{\sqrt{3} }{2}[/tex]
∴, cos A - cos B = 0.5 - 0.866
I.e cos A - cos B = - 0.366
So, Left hand side ≠ Right hand side
Since while equating the values of angle A and b in the given equation on both sides, we get that the value of both sides are not equal , Thus we can say that the given equation is not equal to each other .
Hence given equation is never possible i.e cos ( A - B ) ≠ cos A - cos B Answer
