How do you solve tan^2x-2sec x+1=0 for 0°<=x<=360° ?

1 Answer
Sep 29, 2015

x=60^@,x=300^@

Explanation:

As tan^2(x)=sec^2(x)-1 we can replace the tan^2(x) in the initial equation.

This leaves us with;

sec^2(x)-1-2sec(x)+1=0

After combining like terms the resulting formulae is:

sec^2(x)-2sec(x)=0

We can then factorise by sec(x) to yield;

sec(x)(sec(x)-2)=0

By the null factor law we can then establish two possible solutions for x: when sec(x)=0 or when sec(x)=2

As the secant of x can never equal zero this possibility can be discounted which leaves sec(x)=2.

To solve for sec(x)=2 first we take the reciprocal of each side;

cos(x)=1/2

Now the values of x that satisfy this equality that are within the domain [0^@,360^@] are; x=60^@,x=300^@.

Hope this helps :)