Question 1166005
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{{{2tan(x)^2=3sec(x)-3}}}<br>
Use a basic trig identity to write {{{tan(x)^2}}} in terms of sec(x) to get a quadratic equation in sec(x):<br>
{{{2(sec(x)^2-1) = 3sec(x)-3}}}
{{{2sec(x)^2-2 = 3sec(x)-3}}}
{{{2sec(x)^2-3sec(x)+1 = 0}}}
{{{(2sec(x)-1)(sec(x)-1) = 0}}}<br>
{{{sec(x) = 1/2}}} OR {{{sec(x) = 1}}}<br>
The value of sec(x) is never 1/2, so the only solutions are for sec(x)=1.<br>
But sec(x)=1 means cos(x)=1; cos(x)=1 means the angle is any integer multiple of 2pi.<br>
ANSWER: {{{x = 2k(pi)}}}, k an integer.<br>