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
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