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tanA+tanB+tanC
Asked by girishzene | 03 Sep, 2021, 05:14: AM
answered-by-expert Expert Answer
A, B and C are angles of triangle
 
tan(A) + tan(B) + tan(C) = tan(A) + tan(B) + tan[ 180 - ( A + B ) ] 
 
tan(A) + tan(B) + tan(C) = tan(A) + tan(B)  - tan ( A + B ) 
 
begin mathsize 14px style L H S space space equals space tan left parenthesis A right parenthesis space plus space tan left parenthesis B right parenthesis space minus space fraction numerator tan left parenthesis A right parenthesis space plus tan left parenthesis B right parenthesis space over denominator 1 space minus space tan left parenthesis A right parenthesis space tan left parenthesis B right parenthesis space end fraction space space space space end style 
begin mathsize 14px style L H S space equals fraction numerator tan left parenthesis A right parenthesis space minus space tan squared left parenthesis A right parenthesis space tan left parenthesis B right parenthesis space plus tan left parenthesis B right parenthesis minus space tan left parenthesis A right parenthesis space tan squared left parenthesis B right parenthesis space minus tan left parenthesis A right parenthesis space minus tan left parenthesis B right parenthesis over denominator 1 minus tan left parenthesis A right parenthesis space tan left parenthesis B right parenthesis end fraction space end style
begin mathsize 14px style L H S space equals space minus space tan left parenthesis A right parenthesis space tan left parenthesis B right parenthesis fraction numerator tan left parenthesis A right parenthesis space plus tan left parenthesis B right parenthesis space over denominator 1 minus tan left parenthesis A right parenthesis space tan left parenthesis B right parenthesis end fraction space equals space minus space tan left parenthesis A right parenthesis space tan left parenthesis B right parenthesis space tan left parenthesis A plus B right parenthesis end style
LHS = - tan(A) tan(B) tan [ 180 - C ] = tan(A) tan(B) tan(C)
 
Hence we get , tan(A) + tan(B) + tan(C) = tan(A) tan(B) tan(C)
 
Answered by Thiyagarajan K | 16 Sep, 2021, 23:17: PM
JEE main - Maths
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Asked by ssn | 09 Jun, 2022, 07:31: AM
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JEE main - Maths
Asked by girishzene | 03 Sep, 2021, 05:14: AM
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JEE main - Maths
Asked by azizrajil03 | 28 Feb, 2019, 15:54: PM
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