Question

in triangle ABC tan(A-B+C)=?​

Answer 1

Step-by-step explanation:

A+B+C=180 so that

B+C=180-A

A-B-C=A-(B+C)=A-(180-A)=2A-180

tan(x-y)=(tanx-tany)/(1+tanxtany)

tan(2A-180)=(tan2A-tan(180))/(1_+tan2Atan(180))=tan2A/1-tan2A) since tan(180)=-1

Answer 2

tan(π-2B)

Step-by-step explanation:

In tri. ABC , A+B+C=π

Adding -2B on both sides

A+B+C-2B=π-2B

A-B+C=π-2B

Taking tangent of it we will get the answer

tan(A-B+C)=tan(π-2B)

= -tan2B