Answer:
2csc(2x)
Explanation:
When simplifying the given expression, we can start by finding a common denominator for the fractions. The common denominator for sin x and cos x is cos x * sin x.
Rewriting the expression using the common denominator, we have:
(sin x * sin x)/(cos x * sin x) + (cos x * cos x)/(sin x * cos x)
Simplifying the fractions, we get:
sin^2(x)/(cos x * sin x) + cos^2(x)/(sin x * cos x)
Now, let's simplify each fraction individually:
sin^2(x)/(cos x * sin x) can be simplified to (sin x / cos x)
cos^2(x)/(sin x * cos x) simplifies to (cos x / sin x)
Now, combining the simplified fractions, we have:
(sin x / cos x) + (cos x / sin x)
To combine these fractions, we need a common denominator, which is cos x * sin x:
[(sin x * sin x) + (cos x * cos x)] / (cos x * sin x)
Using the Pythagorean identity sin^2(x) + cos^2(x) = 1, we can simplify the numerator:
(1) / (cos x * sin x)
Therefore, the simplified form of the expression is 1 / (cos x * sin x), or 2csc(2x)