Verify the identity #sin (α + β) sin (α - β) = #?

1 Answer
Abhishek K.
Apr 17, 2018

#rarrsin(alpha+beta)*sin(alpha-beta)=sin^2alpha-sin^2beta#

Explanation:

#rarrsin(alpha+beta)*sin(alpha-beta)#

#=1/2[2sin(alpha+beta)sin(alpha-beta)]#

#=1/2[cos(alpha+beta-(alpha-beta))-cos(alpha+beta+alpha-beta)]#

#=1/2[cos2beta-cos2alpha]#

#=1/2[1-2sin^2beta-(1-2sin^2alpha)]#

#=sin^2alpha-sin^2beta#

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