Prove that

√1+cosø/1 -cosø + √1-cosø/1+cosø = 2cosecø

Asked by Sujalgoyal | 20th Sep, 2020, 09:30: AM

Expert Answer:

To prove that √1+cosø/1 -cosø + √1-cosø/1+cosø = 2cosecø
LHS equals square root of fraction numerator 1 plus cosϕ over denominator 1 minus cosϕ end fraction end root plus square root of fraction numerator 1 minus cosϕ over denominator 1 plus cosϕ end fraction end root
equals square root of fraction numerator open parentheses 1 plus cosϕ close parentheses squared over denominator 1 minus cos squared straight ϕ end fraction end root plus square root of fraction numerator open parentheses 1 minus cosϕ close parentheses squared over denominator 1 minus cos squared straight ϕ end fraction end root
equals fraction numerator 1 plus cosϕ over denominator sinϕ end fraction plus fraction numerator 1 minus cosϕ over denominator sinϕ end fraction
equals fraction numerator 2 cos squared begin display style straight ϕ over 2 end style over denominator sinϕ end fraction plus fraction numerator 2 sin squared begin display style straight ϕ over 2 end style over denominator sinϕ end fraction
equals fraction numerator 2 open parentheses cos squared straight ϕ over 2 plus sin squared straight ϕ over 2 close parentheses over denominator sinϕ end fraction
equals 2 over sinϕ
equals 2 cosecϕ

Answered by Renu Varma | 24th Sep, 2020, 11:09: AM