Make cos (-x+y) as a trigonometric ration of ( x - y )

Question

Make
`cos (-x+y)` as a trigonometric ration of ( x - y )

Answer 1

To make cos(-x+y) as a trigonometric ratio of (x-y), we can use the following identity:

cos(-x+y) = cos(-x)cos(y) + sin(-x)sin(y)

Then, we can use the properties of cosine and sine functions to simplify the expression:

cos(-x) = cos(x) and sin(-x) = -sin(x)

cos(-x+y) = cos(x)cos(y) - sin(x)sin(y)

Now, we can use another identity to rewrite the expression in terms of (x-y):

cos(x)cos(y) - sin(x)sin(y) = cos(x-y)

Therefore, cos(-x+y) = cos(x-y) as a trigonometric ratio of (x-y).

Explanation: