Rewrite the expression in terms of the given function or functions.

Question

csc(x) +tan² (x) csc (x); cos x and sin x

Answer 1

csc x + tan² x csc x = 1/sin x + (sin x)²/(cos x)² · 1/sin x  (express in terms of sin x and cos x)

 

                             = 1/sin x + sin x / cos² x                    (cancel sin x)

 

                             = (cos² x + sin² x)/(sin x cos² x)        (common denominator)

 

                             = 1/(sin x cos² x)                              (Pythagorean identity)

 

                             = (1/sin x)(1/cos² x)                          (break up the fraction as a product)

 

                             = csc x sec x                                     (use basic identities to rewrite)

 

I hope this will be of use to you.