# Thread:

1. ## Sin, sec and cosine.

If sec^2(x) – 1 = sin(x) , which one of the following is a possible value for x?

how do you do this?

The choices are

a) - $\frac{\pi}{2}$

b)= $\frac{\pi}{4}$

c) 0

d) $\frac{\pi}{2}$

e) $\frac{\pi}{4}$

thanks in advance!

2. Originally Posted by fabxx
The choices are

a) - $\frac{\pi}{2}$

b)= $\frac{\pi}{4}$

c) 0

d) $\frac{\pi}{2}$

e) $\frac{\pi}{4}$

thanks in advance!
see, by inspection, 0 works. $\sec^2 0 - 1 = 1 - 1 = 0 = \sin 0$

note that the left hand side (which is actually $\tan^2 x$) is an even function, so if (a) and (b) don't work, (d) and (e) would give the same answer and hence not work either. (c) being 0 catches your eye though, and i would test that first, and what do you know, it worked!

doing this with the algebra would be a bit more complicated and time consuming. so just do the check. you have to check at most 3 values, which you can do pretty quickly if you memorized the trig values for the special angles.
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