What is tan theta+sec theta=1?

Question

anonymous · Answer

are you looking for what theta is?

anonymous · Answer

no its sys solve the eqution on the interval 0<theta(sign)<2pie

anonymous · Answer

*says

anonymous · Answer

yea you need the values of theta that will give you 1

anonymous · Answer

the choices are 0, 5pie/4,pie/4 and no solution

tkhunny · Answer

First, "pie" is for eating.  "pi" is for math.

$\tan(\theta) + \sec(\theta) = 1$

$\dfrac{\sin(\theta)}{\cos(\theta)} + \dfrac{1}{\cos(\theta)} = 1$

Notice that $\cos(\theta) = 0$ is NOT acceptable, no matter what else we do.

$\dfrac{\sin(\theta)+1}{\cos(\theta)} = 1$

$\sin(\theta) + 1 = \cos(\theta)$

$\sin(\theta) - \cos(\theta) + 1 = 0$

There are a couple of ways to go from here.  What do you suggest?  Please show your work.