csc^2x secx/sec^2x+csc^2x
simplify.
question is ambiguous
is it
csc^2x secx/sec^2x+csc^2x
or
csc^2x secx/(sec^2x+csc^2x )
To simplify the expression csc^2x secx / sec^2x + csc^2x, we can start by manipulating the trigonometric identities of csc and sec.
Recall that:
- csc^2x = 1/sin^2x
- sec^2x = 1/cos^2x
Let's substitute these identities into the expression:
csc^2x secx / sec^2x + csc^2x
= (1/sin^2x) * (1/cosx) / (1/cos^2x) + (1/sin^2x)
= (1/sin^2x) * (1/cosx) * (cos^2x/1) + (1/sin^2x)
= (1/cosx) * (cos^2x/sin^2x) + (1/sin^2x)
= cos^2x / sin^2x + (1/sin^2x)
Notice that sin^2x is a common denominator for the two fractions. We can now add the fractions together:
= (cos^2x + 1) / sin^2x
Therefore, the simplified expression is (cos^2x + 1) / sin^2x.