Question

3. If A + B + C = 180°, prove that :
tan 2A + tan 2B + tan 2C = tan 2A tan 2B tan 2C.​

Answer 1

Step-by-step explanation:

A+B+C=180

2A+2B+2C=360

tan(2A+2B)=tan(360-2C)

(tan2A+tan2B)/1-tan2Atan2B =(tan360-tan2C)/1+tan360tan2C

tan2A+tan2B/1-tan2Atan2B= -tan2C

tan2A+tan2B= -tan2C+tan2Atan2Btan2C

tan2A+tan2B+tan2C= tan2Atan2Btan2C

Hence prooved

Answer 2

Step-by-step explanation:

A+B+C=180

2A+2B+2C=360

tan(2A+2B)=tan(360-2C)

(tan2A+tan2B)/1-tan2Atan2B =(tan360-tan2C)/1+tan360tan2C

tan2A+tan2B/1-tan2Atan2B= -tan2C

tan2A+tan2B= -tan2C+tan2Atan2Btan2C

tan2A+tan2B+tan2C= tan2Atan2Btan2C

Hence prooved