Cot A/1-tan A + tan A/1-Cot A

Asked by Srini | 19th Jun, 2017, 07:54: PM

Expert Answer:

begin mathsize 16px style fraction numerator cotA over denominator 1 minus tanA end fraction plus fraction numerator tanA over denominator 1 minus cotA end fraction
equals fraction numerator cotA over denominator 1 minus tanA end fraction plus fraction numerator tanA over denominator 1 minus begin display style 1 over tanA end style end fraction
equals fraction numerator 1 over tanA over denominator 1 minus tanA end fraction plus fraction numerator tanA over denominator begin display style fraction numerator tan straight A minus begin display style 1 end style over denominator tan straight A end fraction end style end fraction
equals fraction numerator 1 over denominator tanA open parentheses 1 minus tanA close parentheses end fraction plus fraction numerator tan squared straight A over denominator tanA minus 1 end fraction
equals fraction numerator 1 over denominator tanA open parentheses 1 minus tanA close parentheses end fraction minus fraction numerator tan squared straight A over denominator 1 minus tanA end fraction
equals fraction numerator 1 over denominator 1 minus tanA end fraction open parentheses 1 over tanA minus tan squared straight A close parentheses
equals fraction numerator 1 over denominator 1 minus tanA end fraction open parentheses fraction numerator 1 minus tan cubed straight A over denominator tanA end fraction close parentheses
equals fraction numerator open parentheses 1 minus tanA close parentheses open parentheses 1 plus tan squared straight A plus tanA close parentheses over denominator tanA open parentheses 1 minus tanA close parentheses space end fraction space space space space space space space space space space space space open square brackets Using space straight a cubed minus straight b cubed equals open parentheses straight a minus straight b close parentheses open parentheses straight a squared plus ab plus straight b squared close parentheses close square brackets
equals fraction numerator 1 plus tan squared straight A plus tanA over denominator tanA end fraction
equals fraction numerator sec squared straight A plus tanA over denominator tanA end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets 1 plus tan squared straight A equals sec squared straight A close square brackets
equals fraction numerator sec squared straight A over denominator tanA end fraction plus tanA over tanA
equals fraction numerator 1 over denominator cos squared straight A end fraction cross times cosA over sinA plus 1 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets secA equals 1 over cosA close square brackets
equals 1 over cosAsinA plus 1
equals secAcosecA plus 1
end style

Answered by Sneha shidid | 20th Jun, 2017, 08:50: AM