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ICSE Class 10 Answered

1+sinA/cosecA-cotA-1-sinA/cosecA+cotA=2(1+cotA)
Asked by m_shailander | 30 Dec, 2018, 12:30: PM
answered-by-expert Expert Answer
I hope the posted question is as given below
 
begin mathsize 12px style p r o v e space t h a t space fraction numerator 1 plus sin A over denominator cos e c space A space minus space c o t space A end fraction space minus space fraction numerator 1 space minus space sin A over denominator cos begin display style e end style begin display style c end style begin display style space end style begin display style A end style begin display style space end style begin display style plus end style begin display style space end style begin display style c end style begin display style o end style begin display style t end style begin display style A end style end fraction space equals space 2 left parenthesis 1 plus c o t space A right parenthesis end style
when mathematical expression has division symbol, use paranthesis to eliminate any ambiguity of denominator terms.
Otherwise send image of the question.
 
begin mathsize 12px style L H S space equals space space fraction numerator 1 plus sin A over denominator cos e c space A space minus space c o t space A end fraction space minus space fraction numerator 1 space minus space sin A over denominator cos begin display style e end style begin display style c end style begin display style space end style begin display style A end style begin display style space end style begin display style plus end style begin display style space end style begin display style c end style begin display style o end style begin display style t end style begin display style A end style end fraction space
sin c e space space space space left parenthesis space cos e c squared A space minus space c o t squared A right parenthesis space equals space 1 comma space w e space h a v e space
L H S space equals space left parenthesis 1 plus sin space A right parenthesis left parenthesis space cos e c space A space plus space c o t space A right parenthesis space minus space open parentheses 1 space minus space sin A close parentheses open parentheses cos e c space A space minus space c o t space A close parentheses
L H S space equals space cos e c A space plus space sin A cos e c A space plus space c o t A space plus space sin A c o t A space minus space cos e c A space plus sin A cos e c A space plus space c o t A space minus sin A space c o t A
A f t e r space c a n c e l l i n g space space o p p o s i t e space t e r m s comma
L H S space equals space 2 sin A cos e c A plus 2 c o t A space equals space 2 left parenthesis 1 plus c o t A right parenthesis
end style
Answered by Thiyagarajan K | 30 Dec, 2018, 02:36: PM
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