how do u prove that 2- sinx = (3+cosx^2)/(2+sinx)

Question

How is this proved, please provide steps

Answer 1

Question: how do u prove that 2- sinx = (3+cosx^2)/(2+sinx)

Use the difference of two squares.

(2 + sinx)(2 - sinx) = 2^2 - sin^2(x)

(2 + sinx)(2 - sinx) = 4 - (1 - cos^2(x))

(2 + sinx)(2 - sinx) = 3 + cos^2(x)

(2 - sinx) = (3 + cos^2(x))/(2 + sinx)