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ICSE Class 10 Answered

PROVE THAT SinØ—CosØ+1 / SinØ+CosØ—1 = 1/ secØ—TanØ  
Asked by siddharthjaiswal1122 | 01 Jul, 2018, 02:52: PM
answered-by-expert Expert Answer
begin mathsize 16px style To space prove space fraction numerator sin empty set space minus space cos empty set space plus space 1 space over denominator sin empty set plus space cos empty set space minus space 1 space end fraction space equals space fraction numerator 1 over denominator sec empty set space minus space tan empty set end fraction
straight L. straight H. straight S space equals space fraction numerator begin display style sin empty set space minus space cos empty set space plus space 1 space end style over denominator begin display style sin empty set plus space cos empty set space minus space 1 space end style end fraction
space space space space space space space space space space equals space fraction numerator tan begin display style empty set end style begin display style space end style begin display style minus end style begin display style space end style begin display style 1 end style begin display style space end style begin display style plus end style begin display style space end style begin display style sec end style begin display style empty set end style over denominator tan begin display style empty set end style begin display style space end style begin display style plus end style begin display style space end style begin display style 1 end style begin display style space end style begin display style minus end style begin display style space end style begin display style sec end style begin display style empty set end style end fraction
space space space space space space space space space space equals fraction numerator begin display style left parenthesis tan empty set space space plus space sec empty set right parenthesis space minus 1 end style over denominator begin display style left parenthesis end style tan begin display style empty set end style begin display style space end style begin display style minus end style begin display style space end style begin display style sec end style begin display style empty set right parenthesis plus space 1 end style end fraction
space space space space space space space space space space equals space fraction numerator begin display style left parenthesis tan empty set space space plus space sec empty set right parenthesis space minus 1 end style over denominator begin display style left parenthesis tan empty set space minus space sec empty set right parenthesis plus space 1 end style end fraction cross times space fraction numerator left parenthesis tan empty set space minus space sec empty set right parenthesis over denominator left parenthesis tan empty set space minus space sec empty set right parenthesis end fraction
space space space space space space space space space space equals space space fraction numerator left parenthesis tan squared empty set space space minus space space sec squared empty set right parenthesis space minus left parenthesis tan empty set space minus space sec empty set right parenthesis over denominator begin display style left square bracket end style left parenthesis tan empty set space minus space sec empty set right parenthesis plus space 1 right square bracket left parenthesis tan empty set space minus space sec empty set right parenthesis end fraction
space space space space space space space space space space equals space fraction numerator negative 1 space minus space tan empty set space plus space sec empty set over denominator left square bracket left parenthesis tan empty set space minus space sec empty set right parenthesis plus space 1 right square bracket left parenthesis tan empty set space minus space sec empty set right parenthesis end fraction
space space space space space space space space space space space equals space fraction numerator negative 1 over denominator left parenthesis tan empty set space minus space sec empty set right parenthesis end fraction space
space space space space space space space space space space space equals space fraction numerator 1 over denominator sec empty set space minus space tan empty set end fraction
space space space space space space space space space space space space equals space straight R. straight H. straight S
end style
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