prove that 1-sinA-cosA/cosA-sinA-1=1-sinA/cosA
Answers
Answer:
TO prove:- Prove that 1+cosA+sinA/1+cosA-sinA = 1+sinA/cosA
Consider space LHS
fraction numerator 1 plus cosA plus sinA over denominator 1 plus cosA minus sinA end fraction
equals fraction numerator 1 plus cosA plus sinA over denominator 1 plus cosA minus sinA end fraction cross times fraction numerator 1 plus cosA plus sinA over denominator 1 plus cosA plus sinA end fraction
equals fraction numerator open parentheses open parentheses 1 plus cosA close parentheses plus sinA close parentheses squared over denominator open parentheses 1 plus cosA close parentheses squared minus sin squared straight A end fraction
equals fraction numerator 1 plus cos squared straight A plus 2 cosA plus sin squared straight A plus 2 sinA open parentheses 1 plus cosA close parentheses over denominator 1 plus cos squared straight A plus 2 cosA minus sin squared straight A end fraction
equals fraction numerator 1 plus cos squared straight A plus sin squared straight A plus 2 cosA plus 2 sinA open parentheses 1 plus cosA close parentheses over denominator cos squared straight A plus 2 cosA plus 1 minus sin squared straight A end fraction
equals fraction numerator 2 plus 2 cosA plus 2 sinA open parentheses 1 plus cosA close parentheses over denominator 2 cos squared straight A plus 2 cosA end fraction
equals fraction numerator 1 plus cosA plus sinA open parentheses 1 plus cosA close parentheses over denominator cos squared straight A plus cosA end fraction
equals fraction numerator open parentheses 1 plus cosA close parentheses open parentheses 1 plus sinA close parentheses over denominator cosA open parentheses 1 plus cosA close parentheses end fraction
equals fraction numerator 1 plus sinA over denominator cosA end fraction
Hence comma space fraction numerator 1 plus cosA plus sinA over denominator 1 plus cosA minus sinA end fraction equals fraction numerator 1 plus sinA over denominator cosA end fraction
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