Question

if tanA=4/7,tanB=1/7,tanC=1/8 so prove that A+B+C=45°

Answer 1

tan A = 4/7
A= tan inverse 4/7
tan B = 1/7
B= tan inverse 1/7
tan C = 1/8
C = tan inverse 1/8
A+B = tan inverse A + tan inverse B
= tan inverse 4/7 + tan inverse 1/7
= tan inverse [ (4/7+1/7) / ( 1-4/7 . 1/7) ]
= tan inverse ( 5/7. 49/45)
= tan inverse (7/9)
A+B+C= tan inverse 7/9 + tan inverse 1/8
= tan inverse [ ( 7/9+1/8) / (1-7/9 .1/8)]
= tan inverse [ {(56+9)/72} / {(72-7/72)}]
= tan inverse (65/65)
= tan inverse (1)
= 1 ....... ........... .... ............ ANS.....