prove that 1+sina-cosa/1+sina+cosa=√1-cos/√1+cosa

Asked by ambarishpatil7 | 28th Sep, 2021, 08:49: PM

Expert Answer:

fraction numerator 1 plus sina minus cosa over denominator 1 plus sina plus cosa end fraction
equals fraction numerator square root of open parentheses 1 plus sina minus cosa close parentheses squared end root over denominator square root of open parentheses 1 plus sina plus cosa close parentheses squared end root end fraction
equals fraction numerator square root of 1 plus sin squared straight a plus cos squared straight a plus 2 sina minus 2 cosa minus 2 sinacosa end root over denominator square root of 1 plus sin squared straight a plus cos squared straight a plus 2 sina plus 2 cosa plus 2 sinacosa end root end fraction
equals fraction numerator square root of 1 plus sina minus cosa minus sinacosa end root over denominator square root of 1 plus sina plus cosa plus sinacosa end root end fraction
equals fraction numerator square root of open parentheses 1 plus sina close parentheses open parentheses 1 minus cosa close parentheses end root over denominator square root of open parentheses 1 plus sina close parentheses open parentheses 1 plus cosa close parentheses end root end fraction
equals square root of fraction numerator 1 minus cosa over denominator 1 plus cosa end fraction end root

Answered by Renu Varma | 1st Oct, 2021, 12:35: PM