- Thread starter
- #1

#### sweatingbear

##### Member

- May 3, 2013

- 91

By squaring and using trigonometric identities on the given equation, one can arrive at

\(\displaystyle \frac {1- \sin x}{1 + \sin x} = 4\)

The unknown expression \(\displaystyle z\) can, by squaring, be written as

\(\displaystyle z^2 = \frac {1 + \sin x}{1 - \sin x} = \frac 14 \)

and thus

\(\displaystyle z = \pm \frac 12\)

However I am unable to rule out the incorrect value for \(\displaystyle z\); how can I from here confidently find the actual correct value for \(\displaystyle z\)?

Another way to solve this is to multiply \(\displaystyle z\) with \(\displaystyle \frac 1{\cos x} - \tan x\) and expand to obtain \(\displaystyle z = \frac 12\). Sure it works and is unambiguous, but I persistently want to be able to obtain the same answer through my previous approach (and thus get better at analyzing the underpinning algebra).

Forum help me rule out the solution \(\displaystyle z = - \frac 12\) from my previous solution.