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ICSE Class 10 Answered

1.Prove that- 1+sinx-cos×/1+sinx-cosx = 1-cos²x/1+cosx  
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Asked by heenasatra17 | 06 Jan, 2019, 09:49: AM
answered-by-expert Expert Answer
I hope the question is to prove
begin mathsize 12px style L e t space u s space u s e space t h e space s y m b o l s comma space space c space equals space cos theta space space a n d space s space equals space sin theta
H e n c e space L H S space equals space fraction numerator 1 minus cos theta plus sin theta over denominator 1 plus sin theta plus cos theta end fraction space equals space fraction numerator 1 minus c plus s over denominator 1 plus s plus c end fraction cross times fraction numerator open parentheses 1 plus s minus c close parentheses over denominator open parentheses 1 plus s minus c close parentheses end fraction space equals space fraction numerator 2 plus 2 s minus 2 c minus 2 c s over denominator open parentheses 1 plus s close parentheses squared minus c squared end fraction space equals space fraction numerator 2 left parenthesis 1 plus s right parenthesis left parenthesis 1 minus c right parenthesis over denominator 1 plus s squared plus 2 s minus c squared end fraction

L H S space equals space fraction numerator 2 left parenthesis 1 plus s right parenthesis left parenthesis 1 minus c right parenthesis over denominator 2 s squared plus 2 s end fraction space equals space fraction numerator 1 minus c over denominator s end fraction space equals space fraction numerator left parenthesis 1 minus c right parenthesis over denominator s end fraction cross times fraction numerator open parentheses 1 plus c close parentheses over denominator open parentheses 1 plus c close parentheses end fraction space equals space fraction numerator open parentheses 1 space minus space c squared close parentheses over denominator s cross times left parenthesis 1 plus c right parenthesis end fraction space equals space fraction numerator open parentheses 1 minus cos squared theta close parentheses over denominator sin theta space cross times open parentheses 1 plus cos theta close parentheses end fraction
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Answered by Thiyagarajan K | 06 Jan, 2019, 11:19: AM
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