Question #19476

1 Answer
Feb 14, 2017

See answer below.

Explanation:

#secy+tany=1/cosy+siny/cosy=(cosy+cosysiny)/cos^2y=#

#=(cosy(1+siny))/(1-sin^2y)=(cosy(cancel(1+siny)))/((cancel(1+siny))(1-siny))=cosy/(1-siny)#

Let's break this down:

  1. Rewrite #secy# and #tany# as #1/cosy# and #siny/cosy#
  2. Add the two fractions
  3. Take a factor of #cosy# from the numerator
  4. Rewrite #cos^2y# as #1-sin^2y# using #cos^2y+sin^2y=1#
  5. Rewrite #1-sin^2y# using the difference of two squares identity
  6. Cancel the common factors