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If cosecΦ + cotΦ = p, then prove that cosΦ = p²-1/p²+1.
Asked by pdcavita | 18 Nov, 2017, 01:01: PM
answered-by-expert Expert Answer
begin mathsize 16px style fraction numerator straight p squared minus 1 over denominator straight p squared plus 1 end fraction equals fraction numerator begin display style open parentheses cos begin display style ec end style begin display style space end style begin display style empty set end style begin display style plus end style begin display style cot end style begin display style space end style begin display style empty set end style close parentheses squared end style begin display style minus end style begin display style 1 end style over denominator open parentheses cosec space empty set plus cot space empty set close parentheses squared plus 1 end fraction equals fraction numerator cos begin display style begin display style ec end style squared end style begin display style space end style begin display style empty set end style begin display style plus end style begin display style begin display style cot end style squared end style begin display style space end style begin display style empty set end style begin display style plus end style begin display style 2 end style begin display style space end style begin display style cosec end style begin display style space end style begin display style empty set end style begin display style space end style begin display style cot end style begin display style space end style begin display style empty set end style begin display style minus end style begin display style 1 end style over denominator cosec squared space empty set plus cot squared space empty set plus 2 space cosec space empty set space cot space empty set plus 1 end fraction equals fraction numerator begin display style left parenthesis cos ec squared space empty set minus 1 right parenthesis plus cot squared space empty set plus 2 space cosec space empty set space cot space empty set end style over denominator cosec squared space empty set plus 2 space cosec space empty set space cot space empty set plus left parenthesis 1 plus cot squared space empty set right parenthesis end fraction equals fraction numerator begin display style cot squared space empty set plus cot squared space empty set plus 2 space cosec space empty set space cot space empty set end style over denominator cosec squared space empty set plus 2 space cosec space empty set space cot space empty set plus cosec squared space empty set end fraction equals fraction numerator begin display style 2 cot squared space empty set plus 2 space cosec space empty set space cot space empty set end style over denominator 2 cosec squared space empty set plus 2 space cosec space empty set space cot space empty set end fraction equals fraction numerator begin display style 2 cot space empty set left parenthesis cot space empty set plus cosec space empty set right parenthesis end style over denominator 2 cosec empty set left parenthesis cosec space empty set plus cot space empty set right parenthesis end fraction equals fraction numerator cot space empty set over denominator cosec empty set end fraction equals fraction numerator cos begin display style space end style begin display style empty set end style over denominator sin begin display style space end style begin display style empty set end style begin display style cross times end style begin display style fraction numerator 1 over denominator sin begin display style space end style begin display style empty set end style end fraction end style end fraction equals cos space empty set end style
Answered by Rashmi Khot | 05 Dec, 2017, 04:00: PM

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