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CBSE Class 10 Answered

secA = x+1/4x, prove that secA + tanA = 2x or 1/2x.
Asked by sangobhattad | 14 Feb, 2019, 06:18: PM
answered-by-expert Expert Answer
begin mathsize 12px style s e c space A space equals space x plus fraction numerator 1 over denominator 4 x end fraction space equals space fraction numerator 4 x squared plus 1 over denominator 4 x end fraction
cos A space equals space fraction numerator 4 x over denominator 4 x squared plus 1 end fraction space semicolon space space space
sin A space equals space square root of 1 space minus space cos squared A end root space equals space square root of 1 minus fraction numerator 16 x squared over denominator open parentheses 4 x squared plus 1 close parentheses squared end fraction end root space space equals space square root of fraction numerator open parentheses 4 x squared plus 1 close parentheses squared minus 16 x squared over denominator open parentheses 4 x squared plus 1 close parentheses squared end fraction end root space equals space square root of open parentheses 4 x squared minus 1 close parentheses squared over open parentheses 4 x squared plus 1 close parentheses squared end root
sin A space equals space plus-or-minus fraction numerator open parentheses 4 x squared minus 1 close parentheses over denominator 4 x squared plus 1 end fraction
i f space sin A space equals space fraction numerator open parentheses 4 x squared minus 1 close parentheses over denominator 4 x squared plus 1 end fraction space space comma space s e c A space plus space tan A space equals fraction numerator 4 x squared plus 1 over denominator 4 x end fraction space plus space fraction numerator open parentheses 4 x squared minus 1 close parentheses over denominator 4 x end fraction space equals space 2 x
i f space sin A space equals space fraction numerator open parentheses 1 minus 4 x squared close parentheses over denominator 4 x squared plus 1 end fraction space comma space space s e c A space plus space tan A space equals fraction numerator 4 x squared plus 1 over denominator 4 x end fraction space plus space fraction numerator open parentheses 1 minus 4 x squared close parentheses over denominator 4 x end fraction space equals space fraction numerator 1 over denominator 2 x end fraction end style
Answered by Thiyagarajan K | 14 Feb, 2019, 08:47: PM
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