Solve Sec^2x - 1 = 1/cot(x)? Interval of x is [0, 360)

Question

#sec^2#x - 1 = 1 / cot(x)

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Answer 1 · 2018-05-28T04:15:01

#x = 0 or 90#

First, we use Pythagorean identities.

#sec^2(x) - 1 = tan^2(x)#

#tan^2(x) = tan(x)#

We now have a polynomial in #tan(x)#.

#tan^2(x) - tan(x) = 0#

#tan(x)(tan(x)-1) = 0#

So, #tan(x) = 0# or #tan(x) = 1#.

#x = 0 or 90#.