prove that tan inverse 1/3 + tan inverse 1/7 + tan inverse 1/8 = pi/4
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note - tan ^(-1) here means tan inverse
tan ^(-1)(1/3)+tan^(-1)1/7+tan^(-1 )1/8
=tan^(-1)[(1/3+1/7)/(1-1/3×1/7)]+tan^(-1)1/8
=tan^(-1)[{(7+3)/21}/{(21-1)/21}]+tan^(-1)1/8
=tan^(-1)[1/2]+ tan^(-1)1/8
(then the same process
you get)
=tan^(-1)[1]
=pi/4
tan ^(-1)(1/3)+tan^(-1)1/7+tan^(-1 )1/8
=tan^(-1)[(1/3+1/7)/(1-1/3×1/7)]+tan^(-1)1/8
=tan^(-1)[{(7+3)/21}/{(21-1)/21}]+tan^(-1)1/8
=tan^(-1)[1/2]+ tan^(-1)1/8
(then the same process
you get)
=tan^(-1)[1]
=pi/4
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