Question

check true or false : tan A + tan B +tan C = tan A tanB tanC​

Answer 1

Step-by-step explanation:

This statement is true

∴A+B+C=π

∴A+B+C=π∴tan(A+B+C)=tanπ=0

∴A+B+C=π∴tan(A+B+C)=tanπ=0⟹1−tanAtanB−tanBtanC−tanCtanAtanA+tanB+tanC−tanAtanBtanC=0

∴A+B+C=π∴tan(A+B+C)=tanπ=0⟹1−tanAtanB−tanBtanC−tanCtanAtanA+tanB+tanC−tanAtanBtanC=0tanA+tanB+tanC=tanAtanB

Answer 2

Step-by-step explanation:

Given :-

tan A + tan B +tan C = tan A tanB tanC

To find :-

Check whether it is true or false ?

Solution :-

If A, B and C are the three angles in a triangle ABC.

we know that

The sum of all angles in a triangle is 180°

A + B + C = 180°

=> A + B = 180° - C ---------(1)

On taking Tan both sides then

=> Tan ( A+B) = Tan (180° - C)

We know that

Tan (180-X)° = -Tan X°

=> Tan (A+B) = -Tan C

We know that

=>(Tan A + Tan B)/(1-Tan A Tan B) = -Tan C

=> Tan A + Tan B = -Tan C( 1-Tan A Tan B)

=>Tan A+Tan B=-Tan C+Tan A Tan B Tan C

=>Tan A+Tan B+Tan C = Tan A Tan B Tan C

It is true Statement.

Answer:-

Tan A +Tan B+ Tan C = Tan A Tan B Tan C is true .

Used formulae:-

→ Tan (180-X)° = -Tan X°

→ Tan(A+B)=(Tan A + Tan B)/(1-Tan A Tan B)

→The sum of all angles in a triangle is 180°