#sin^2A+sin^2(A-B)+2sinAcosBsin(B-A)=# ?

options are

  1. #sin^2A#
  2. #sin^2B#
  3. #cos^2A#
  4. #cos^2B#

1 Answer
Hriman
Aug 10, 2018

2.

Explanation:

#sin^2A+sin^2(A-B)+2sinAcosBsin(B-A)=#

#sin^2a+(sinacosb-cosasinb)(sinacosb-cosasinb)+2sinacosb(sinbcosa-cosbsina)=#

#sin^2a+sin^2acos^2b-2sinacosasinbcosb+cos^2asin^2b+2sinasinbcosacosb-2cos^2bsin^2a=#

#sin^2a-sin^2acos^2b+cos^2asin^2b=#

#sin^2a(1-cos^2b+cot^2asin^2b)=#

#sin^2asin^2b(1+cot^2a)=#

#sin^2asin^2b(csc^2a)=#

#sin^2asin^2b(1/sin^2a)=#

#sin^2b#

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