Math, asked by Kaffichhabra, 4 months ago

IfA=60°
& B=30. Prove that tan (A+B) = tanAtan B/
I- tanAtan B​

Answers

Answered by assingh
4

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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