Question #6abe5

1 Answer
Jo S.
Oct 25, 2017

Start by writing the LHS as a single fraction, expand and simplify the denominator and then use c^2+s^2=1 to simplify it further.

Explanation:

LHS denominator becomes #(1-sin theta)(1+sin theta)=(1-sin^2 theta)#. Using the pythagorean identity, this is #cos^2 theta#.
The LHS numerator is #(1+sin theta)^2-(1-sin theta)^2#
#=(1+sin theta+1-sin theta)(1+sin theta-1+sin theta)#
#=2(2sin theta)#
#=4sin theta#
So LHS is now #(4sin theta)/cos^2 theta=4sin theta sec^2 theta#

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