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Question Number 210231 by a.lgnaoui last updated on 03/Aug/24
ResoudredansR{acosx−bsinx=c(x≠0)sin(1sinx)=d(−1⩽d⩽+1)
Commented by mr W last updated on 04/Aug/24
theyaretwodifferentequationsforvariablex.theyhavedifferentroots.theycannotbeanequationsystem!eqn.1:acosx−bsinx=ca2+b2cos(x+tan−1ba)=cassume∣c∣⩽a2+b2cos(x+tan−1ba)=ca2+b2⇒x+tan−1ba=2kπ±cos−1ca2+b2⇒x=2kπ−tan−1ba±cos−1ca2+b2eqn.2:sin(1sinx)=d⇒1sinx=kπ+(−1)ksin−1d⇒sinx=1kπ+(−1)ksin−1d⇒x=nπ+(−1)nsin−1(1kπ+(−1)ksin−1d)
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