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ICSE Class 10 Answered

eliminate A if  tan A+sin A=m tan A-sin A=n
Asked by shivasanthosh0804 | 23 Jan, 2019, 06:20: PM
answered-by-expert Expert Answer
tan A + sin A = m ...............(1)
tan A  - sin A = n .................(2)
 
By adding (1) and (2),  2tanA = m+n  or  tanA = (m+n)/2 ..............(3)
 
By subtracting (2) from (1),  2 sinA = m-n  or  sinA = (m-n)/2 .........(4)
 
( tan A )/(sin A) = 1/( cos A)  = (m+n)/(m-n)   or  cos A = (m-n)/(m+n)  ...............(5)
 
we have sin2A + cos2A = 1,
 
hence from eqn.(4) and (3), begin mathsize 12px style fraction numerator left parenthesis m minus n right parenthesis squared over denominator 4 end fraction space plus space fraction numerator begin display style open parentheses m minus n close parentheses squared end style over denominator begin display style open parentheses m plus n close parentheses squared end style end fraction space equals space 1 end style
begin mathsize 12px style open parentheses m squared minus n squared close parentheses squared space plus space 4 left parenthesis m minus n right parenthesis squared space equals space 4 left parenthesis m plus n right parenthesis squared
open parentheses m squared minus n squared close parentheses squared space equals space 4 left parenthesis m plus n right parenthesis squared space minus space 4 left parenthesis m minus n right parenthesis squared space equals space 16 m n
open parentheses m squared minus n squared close parentheses squared space equals space space 16 m n
end style
Answered by Thiyagarajan K | 23 Jan, 2019, 09:37: PM
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