Use the fundamental identities to simplify the expression.
cos^2θ/sin^2θ+cscθsinθ
I got tan^2theta
Nope.
cos/sin = cot
csc * sin = 1
so you have
cot^2 + 1 = csc^2
To simplify the expression cos^2θ/sin^2θ + cscθsinθ using fundamental identities, we can start by working on the first term:
cos^2θ/sin^2θ
Using the Pythagorean identity, cos^2θ = 1 - sin^2θ, we can substitute this into the expression:
(1 - sin^2θ)/sin^2θ + cscθsinθ
Next, let's simplify cscθsinθ. Since cscθ is the reciprocal of sinθ, we can write:
cscθsinθ = 1
Now, we can rewrite the expression:
(1 - sin^2θ)/sin^2θ + 1
Next, let's simplify the first term by distributing the numerator:
1/sin^2θ - sin^2θ/sin^2θ + 1
Simplifying further:
1/sin^2θ - 1 + 1
Finally, combining like terms, we get:
1/sin^2θ
Using the identity csc^2θ = 1/sin^2θ, we can rewrite the expression as:
csc^2θ
So, the simplified form of the given expression is csc^2θ.