3. If A + B + C = 180°, prove that :
tan 2A + tan 2B + tan 2C = tan 2A tan 2B tan 2C.
Answers
Answered by
4
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
Answered by
3
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
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