Expert: Sherry Wallin - 4/1/2010

Question
Solve tansquaredx - secx = -1  given that 0<= x < 360

Answer
Hi Drew~
    There are a number of ways to solve this. The way I solved it was to change everything into cosines:
tan^2 x = sin^2x/cos^2 = (1-cos^2x)/cos^2x
-secx = -1/cosx
-1 = -cosx/cosx
so
tan^2x -secx = -1 -> [(1-cos^2x)/cos^2x-1/cosx + cosx/cosx]  * you need a common denominator of cos^2x:
[(1-cos^2x)-cosx + cos^2x]/cos^2x -> 1-cosx = 0   the cos^2x cancel out
1 = cosx  you can either take the arccosine of both sides to find x or you can ask yourself where is the cosine of an angle equal to 1 in the interval 0<= x <360 and the only time cosine of angle is one is at zero degrees. You can check that in the original equation:
tan^2(0) = 0 and -1/cox(0) = -1 and their sum is -1.

Math Prof