Sahkan dosa identiti (α + β) dosa (α - β) =?

Jawapan:

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

Penjelasan:

#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 #