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CBSE Class 10 Answered

prove that 1 +secA - tanA / 1 + secA + tanA =1-sinA /cosA
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Asked by kumarimanoram8642 | 23 Jun, 2022, 08:58: PM
answered-by-expert Expert Answer
fraction numerator 1 plus sec space straight A space minus space tan space straight A over denominator 1 plus sec space straight A space plus space tan space straight A end fraction equals fraction numerator 1 plus begin display style fraction numerator 1 over denominator cos space straight A end fraction end style space minus space begin display style fraction numerator sin space straight A over denominator cos space straight A end fraction end style over denominator 1 plus fraction numerator 1 over denominator cos space straight A end fraction space space plus fraction numerator sin space straight A over denominator cos space straight A end fraction end fraction equals fraction numerator cos space straight A space plus space 1 space minus space sin space straight A over denominator cos space straight A space plus space 1 space plus space sin space straight A end fraction
equals fraction numerator open parentheses cos space straight A space plus space 1 space minus space sin space straight A close parentheses squared over denominator open parentheses cos space straight A space plus space 1 space plus space sin space straight A close parentheses open parentheses cos space straight A space plus space 1 space minus space sin space straight A close parentheses end fraction
equals fraction numerator cos squared straight A plus 1 plus sin to the power of 2 space end exponent straight A minus 2 cosAsinA plus 2 cosA minus 2 sinA over denominator open parentheses cos space straight A space plus space 1 close parentheses squared space minus space sin squared space straight A end fraction
equals fraction numerator 2 minus 2 cosAsinA plus 2 cosA minus 2 sinA over denominator 1 plus 2 cosA plus cos squared straight A minus 1 plus cos to the power of 2 space end exponent straight A end fraction
equals fraction numerator 2 minus 2 cosAsinA plus 2 cosA minus 2 sinA over denominator 2 cos to the power of 2 space end exponent straight A plus 2 cosA end fraction
equals fraction numerator 1 minus cosAsinA plus cosA minus sinA over denominator open parentheses 1 plus cosA close parentheses cosA end fraction
equals fraction numerator open parentheses 1 plus cosA close parentheses open parentheses 1 minus sinA close parentheses over denominator open parentheses 1 plus cosA close parentheses cosA end fraction
equals fraction numerator 1 minus sinA over denominator cosA end fraction
Answered by Arun | 24 Jun, 2022, 12:56: PM
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