Verify the identity algebraically. sin(theta) csc(theta) - sin^2(theta) = cos^2(theta)

Answer 1

sinθ times cscθ is equal to 1 because cscθ is equal to 1/sinθ

thus we can substitute sinθcscθ with 1 in our equation

then we are left with 1 - sin²θ = cos²θ

by our trig identities we know that sin²θ + cos²θ = 1 so the above statement is true