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CBSE Class 11-science Answered

Prove that: tan A + se A - 1/ tan A - sec A + 1= 1 + sin A/ cos A
Asked by hariom2083 | 05 Jul, 2018, 12:18: AM
answered-by-expert Expert Answer
begin mathsize 16px style To space prove colon
fraction numerator tanA space plus space secA space minus 1 over denominator tanA space minus space secA space plus space 1 end fraction equals space fraction numerator 1 space plus space sinA over denominator cosA end fraction
straight L. straight H. straight S space equals fraction numerator tanA space plus space secA space minus 1 over denominator tanA space minus space secA space plus space 1 end fraction space
space space space space space space space space space space equals fraction numerator tanA space plus space secA space minus space left parenthesis sec squared straight A space minus space tan squared straight A right parenthesis over denominator tanA space minus space secA space plus space 1 end fraction
space space space space space space space space space space equals fraction numerator tanA space plus space secA space minus open square brackets open parentheses secA space minus space tanA close parentheses open parentheses secA space plus space tanA close parentheses close square brackets space over denominator tanA space minus space secA space plus space 1 end fraction
space space space space space space space space space space equals fraction numerator open parentheses secA space plus space tanA close parentheses open parentheses 1 space minus space secA space plus space tanA close parentheses over denominator tanA space minus space secA space plus space 1 end fraction
space space space space space space space space space space equals space 1 over cosA plus space sinA over cosA
space space space space space space space space space space equals space fraction numerator 1 space plus space sinA over denominator cosA end fraction
space space space space space space space space space space equals space straight R. straight H. straight S end style
Answered by Yasmeen Khan | 05 Jul, 2018, 10:53: AM

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