Question

In any triangle ABC prove that tan (a + b) =-tan C

Answer 1

in any triangle, if A, B, C are its angles,

then A+B+C=180°

A+B=180°-C

so, tan(A+B)=tan(180°-C)

as we know that tan(180-x)=-tanx

therefore, tan(180°-C)=-tanC

hence,proved!