Solve the equation $tan^2x=3(3-secx)$ , if $x$ lies in interval $[0^@,360^@)$ ?

Question

2936 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-05T14:43:57

$x$ is $60^@, 101.5^@, 258.5^@$ or $300^@$

As $tan^2x=3(3-secx)$ , we have

$sec^2x-1=9-3secx$

or $sec^2x+3secx-10=0$

or $(secx+5)(secx-2)=0$

Hence $secx=-5$ or $secx=2$ and using tables

$cosx=-0.2=cos101.5^@$ and $cos258.5^@$

or $cosx=0.5=cos60^@$ and $cos300^@$

(as $cos(360^@-A)=cosA$ )

Hence, $x$ is $60^@, 101.5^@, 258.5^@$ or $300^@$

Solve the equation tan^2x=3(3-secx)tan^2x=3(3-secx), if xx lies in interval [0^@,360^@)[0^@,360^@)?