ICSE Class 10 Answered
eliminate A if
tan A+sin A=m
tan A-sin A=n
Asked by shivasanthosh0804 | 23 Jan, 2019, 18:20: PM
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](https://images.topperlearning.com/topper/tinymce/cache/26b1c6107f663662c0992a7f7abe8fc6.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/26b1c6107f663662c0992a7f7abe8fc6.png)
![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](https://images.topperlearning.com/topper/tinymce/cache/992ca51e03d2a7c631d2848967262e15.png)
Answered by Thiyagarajan K | 23 Jan, 2019, 21:37: PM
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