To express the given expression tan(1x) * cos(1y) in terms of x and y only, we can start by using the definitions of the tangent and cosine functions.
Firstly, we can rewrite the tangent function. We know that:
- tan(θ) = sin(θ) / cos(θ)
Applying this to tan(1x), we can write:
tan(1x) = sin(1x) / cos(1x)
Now, substituting this back into our original expression gives:
tan(1x) * cos(1y) = (sin(1x) / cos(1x)) * cos(1y)
This can be simplified to:
sin(1x) * cos(1y) / cos(1x)
So, the expression tan(1x) * cos(1y) can be rewritten in terms of x and y as:
sin(1x) * cos(1y) / cos(1x)
In summary, by using the trigonometric identity for tangent, we’ve successfully rewritten the expression in terms of x and y.