( 1/ ( secsquaretheta - cossquaretheta) + 1/ ( cosecsquaretheta - sinsquaretheta) * sinsquaretheta*cossquaretheta = ( 1 - sinsquaretheta*cossquaretheta)/ ( 2 + sinsquaretheta * cossquaretheta)

Asked by Sthitaprajna Mishra | 7th Sep, 2014, 03:59: PM

Expert Answer:

open square brackets fraction numerator 1 over denominator s e c squared theta minus cos squared theta end fraction plus fraction numerator 1 over denominator c o s e c squared theta minus sin squared theta end fraction close square brackets. sin squared theta. cos squared theta space equals fraction numerator 1 minus sin squared theta. cos squared theta over denominator 2 plus sin squared theta. cos squared theta end fraction L H S comma equals open square brackets fraction numerator 1 over denominator begin display style fraction numerator 1 over denominator cos squared theta end fraction end style minus cos squared theta end fraction plus fraction numerator 1 over denominator begin display style fraction numerator 1 over denominator sin squared theta end fraction end style minus sin squared theta end fraction close square brackets. sin squared theta. cos squared theta equals open square brackets fraction numerator cos squared theta over denominator begin display style 1 end style minus cos to the power of 4 theta end fraction plus fraction numerator sin squared theta over denominator 1 minus sin to the power of 4 theta end fraction close square brackets. sin squared theta. cos squared theta equals open square brackets fraction numerator cos squared theta over denominator left parenthesis 1 plus cos squared theta right parenthesis left parenthesis 1 minus cos squared theta right parenthesis end fraction plus fraction numerator sin squared theta over denominator left parenthesis 1 plus sin squared theta right parenthesis left parenthesis 1 minus sin squared theta right parenthesis end fraction close square brackets. sin squared theta. cos squared theta equals open square brackets fraction numerator cos squared theta over denominator left parenthesis 1 plus cos squared theta right parenthesis sin squared theta end fraction plus fraction numerator sin squared theta over denominator left parenthesis 1 plus sin squared theta right parenthesis cos squared theta end fraction close square brackets. sin squared theta. cos squared theta equals fraction numerator cos squared theta. sin squared theta. cos squared theta over denominator left parenthesis 1 plus c o s squared theta right parenthesis sin squared theta end fraction plus fraction numerator sin squared theta. sin squared theta. cos squared theta over denominator left parenthesis 1 plus sin squared theta right parenthesis cos squared theta end fraction equals fraction numerator cos to the power of 4 theta over denominator left parenthesis 1 plus co s squared theta right parenthesis end fraction plus fraction numerator sin to the power of 4 theta over denominator left parenthesis 1 plus sin squared theta right parenthesis end fraction equals fraction numerator cos to the power of 4 theta left parenthesis 1 plus sin squared theta right parenthesis plus sin to the power of 4 theta left parenthesis 1 plus cos squared theta right parenthesis over denominator left parenthesis 1 plus co s squared theta right parenthesis left parenthesis 1 plus sin squared theta right parenthesis end fraction equals fraction numerator cos to the power of 4 theta plus cos to the power of 4 theta sin squared theta plus sin to the power of 4 theta plus sin to the power of 4 theta cos squared theta over denominator 1 plus co s squared theta plus sin squared theta plus sin squared theta. c o s squared theta end fraction equals fraction numerator cos to the power of 4 theta plus sin to the power of 4 theta plus cos to the power of 4 theta sin squared theta plus sin to the power of 4 theta cos squared theta over denominator 1 plus co s squared theta plus sin squared theta plus sin squared theta. c o s squared theta end fraction equals fraction numerator open parentheses cos squared theta close parentheses squared plus open parentheses sin squared theta close parentheses squared plus sin squared theta. cos squared theta left parenthesis sin squared theta plus cos squared theta right parenthesis over denominator 2 plus sin squared theta. c o s squared theta end fraction equals fraction numerator open parentheses cos squared theta plus sin squared theta close parentheses squared minus 2 sin squared theta. cos squared theta plus sin squared theta. cos squared theta.1 over denominator 2 plus sin squared theta. c o s squared theta end fraction left square bracket because left parenthesis a to the power of 4 plus b to the power of 4 right parenthesis equals left parenthesis a squared plus b squared right parenthesis squared minus 2 a squared b squared right square bracket equals fraction numerator 1 minus 2 sin squared theta. cos squared theta plus sin squared theta. cos squared theta over denominator 2 plus sin squared theta. c o s squared theta end fraction equals fraction numerator 1 minus sin squared theta. cos squared theta over denominator 2 plus sin squared theta. c o s squared theta end fraction equals R H S

Answered by Prasenjit Paul | 8th Sep, 2014, 11:06: AM