Given A= 60 degree and B= 30 degree, prove that:
Tan(A-B) = TanA - TanB / 1+ TanA . TanB.
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A = 60 degree
B = 30 degree
from lhs
tan(A - B) = tan(60 - 30° ) = tan30° = 1/√3
from Rhs
tanA - tanB / 1 + tanA . tanB
tan60° - tan30 / 1 + tan60 tan30
√3 - 1/√3 / 1 + √3. 1/√3
3 - 1 / √3 / 2
2/ √3 / 2 = 1/√3
LHS = RHS ..so prooved
B = 30 degree
from lhs
tan(A - B) = tan(60 - 30° ) = tan30° = 1/√3
from Rhs
tanA - tanB / 1 + tanA . tanB
tan60° - tan30 / 1 + tan60 tan30
√3 - 1/√3 / 1 + √3. 1/√3
3 - 1 / √3 / 2
2/ √3 / 2 = 1/√3
LHS = RHS ..so prooved
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