IfA=60°
& B=30. Prove that tan (A+B) = tanAtan B/
I- tanAtan B
Answers
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Topic
Trigonometry
Given
Angle A = 60° and B = 30°
To Prove
tan( A + B ) = tanA.tanB / ( 1 - tanA.tanB )
Method
We will solve for Left Hand Side and equate it with Right Hand Side.
Solving
LHS ( Left Hand Side )
tan( A + B )
tan ( 60° + 30° )
tan 90° = ∞
RHS ( Right Hand Side )
tanA.tanB / ( 1 - tanAtanB )
tan60°.tan30° / ( 1 - tan60°.tan30° )
( tan 60° = √3 )
( tan 30° = 1/√3 )
Putting values,
√3.( 1/√3 ) / ( 1 - √3.( 1/√3 ) )
1 / ( 1 - 1 )
1 / 0
∞
We can observe that LHS = RHS.
Hence, proved.
Learn More :-
Some Formulas
tan ( A + B )
= ( tanA + tanB ) / ( 1 - tanA.tanB )
tan ( A - B )
= ( tanA - tanB ) / ( 1 + tanA.tanB )
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