Ohh.... Tq Q1. Prove that( cosecA - sinA) (secA - cosA) = 1/ tanA - cotA.

Asked by pdcavita | 19th Nov, 2017, 02:11: PM

Expert Answer:

begin mathsize 16px style Mistake space in space question space
prove space that space colon open parentheses cosec space straight A space minus space sin space straight A close parentheses left parenthesis sec space straight A minus space cos space straight A right parenthesis equals fraction numerator 1 over denominator tan space straight A plus cot space straight A end fraction
LHS
open parentheses cosec space straight A space minus space sin space straight A close parentheses left parenthesis sec space straight A minus space cos space straight A right parenthesis
equals open parentheses fraction numerator 1 over denominator sin space straight A end fraction minus sin space straight A close parentheses open parentheses fraction numerator 1 over denominator cos space straight A end fraction minus cos space straight A close parentheses
equals open parentheses fraction numerator 1 minus sin space squared straight A over denominator sin space straight A end fraction close parentheses open parentheses fraction numerator 1 minus cos squared straight A over denominator cos space straight A end fraction close parentheses
equals open parentheses fraction numerator cos squared straight A over denominator sin space straight A end fraction close parentheses open parentheses fraction numerator sin squared straight A over denominator cos space straight A end fraction close parentheses
equals open parentheses cos space straight A cross times sin space straight A close parentheses
RHS
equals fraction numerator 1 over denominator tan space straight A plus cot space straight A end fraction
equals fraction numerator 1 over denominator fraction numerator sinA over denominator cos space straight A end fraction plus fraction numerator cosA over denominator sin space straight A end fraction end fraction
equals fraction numerator cos space straight A space cross times space sin space straight A over denominator sin space squared straight A space plus cos squared space straight A end fraction
equals open parentheses cos space straight A cross times sin space straight A close parentheses
LHS thin space equals space RHS

end style

Answered by Arun | 5th Dec, 2017, 04:17: PM