Answer:
sin 5x cos x - cos 5x sin x = sin(4x)
Step-by-step explanation:
Given that the trigonometric expression,
sin 5x cos x - cos 5x sin x
Here we use the "sum and difference formulas"
Sum and Difference Formulas
sin(A+B)=sin A cos B + cos A sin B
sin(A-B)=sin A cos B - cos A sin B
cos(A+B)=cos A cos B - sin A sin B
cos(A-B)=cos A cos B + sin A sin B
So,
sin 5x cos x - cos 5x sin x = sin (5x - x)
sin 5x cos x - cos 5x sin x = sin(4x)
That's the final answer.
Answer: 
Step-by-step explanation:
Given : A man earned x pesos in 10 days and spent y pesos during each of those days.
i.e. Total earning in 10 days = x
Earning per day =
[By unitary method] (1)
Money spent per day =y (2)
We know that

i.e. Subtract (2) from (1), we get

Hence, the expression to determine how many pesos he saved per day will be:-
