Question 359681
{{{sin(x)+cos(x)=1}}}
{{{sin(x)=1-cos(x)}}}
{{{(sin(x))^2=(1-cos(x))^2}}}
{{{1-(cos(x))^2=1-2cos(x)+cos(x)^2}}}
{{{2(cos(x))^2-2cos(x)=0}}}
{{{cos(x)*(cos(x)-1)=0}}}
Two solutions:
{{{cos(x)=0}}}
{{{x=pi/2}}} and {{{x=(3pi)/2}}}
However at {{{x=(3pi)/2}}}, {{{sin(x)=-1}}} and {{{cos(x)=0}}}
so that {{{sin(x)+cos(x)<>1}}}
Only {{{highlight(x=pi/2)}}} is a valid solution.
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{{{cos(x)-1=0}}}
{{{cos(x)=1}}}
{{{highlight(x=0)}}}