How can I prove that (CSC^2x) (secx) = secx + cscx (cotx) by working the left side only?

Answer 1

(csc² x)(sec x)

1 / (sin² x cos x)

(sin² x + cos² x) / (sin² x cos x)

sin² / (sin² cos x) + cos² x / (sin² x cos x)

(1 / cos x) + (cos² x / (sin² x cos x)

sec x + (cos x / sin x)(1 / sin x)

sec x + (cot x)(csc x)

QED