# How do you solve #sec^2x-2tan^2x=0#?

##### 1 Answer

#### Explanation:

Here, we can use the Pythagorean Identity, which states that

We can substitute this into the original equation to write it just in terms of tangent, instead of with both tangent and secant.

#(sec^2x)-2tan^2x=0" "=>" "(1+tan^2x)-2tan^2x=0#

Simplifying this by combining the

#1-tan^2x=0#

Thus:

#tan^2x=1#

Taking the square root, and remembering both the positive and negative roots:

#tanx=+-1#

Notice that

Similarly,

Combining all these answers, and remembering that they go on forever, we see that

But, the solutions don't stop, and we can generalize them by making a rule. Note that every solution for

This is expressed as

#x=pi/4+(kpi)/2,kinZZ#

Note that