# Trig Identity - I'm so close (i think..)

#### repete

Im still trying to figure out these identities. Ive never had so much trouble with math, ugh. I think I almost figured this one out but I must have taken a wrong turn somewhere. Here is the identity.

$$\displaystyle \frac{1-\sin\theta}{\cos\theta}+\frac{\cos\theta}{1-\sin\theta}=2\sec\theta$$

I started with the left side and used the lcm to get...

$$\displaystyle \frac{1-\sin\theta-\sin\theta+\sin^2\theta+\cos^2\theta}{(1-\sin\theta)(\cos\theta)}$$

Then simplified to get...

$$\displaystyle \frac{2-2\sin\theta}{(1-\sin\theta)(\cos\theta)}$$

and finally...

$$\displaystyle \frac{1-\sin\theta}{\cos\theta}$$

I obviously messed something up somewhere can anyone tell me where I went wrong?

#### e^(i*pi)

MHF Hall of Honor
Im still trying to figure out these identities. Ive never had so much trouble with math, ugh. I think I almost figured this one out but I must have taken a wrong turn somewhere. Here is the identity.

$$\displaystyle \frac{1-\sin\theta}{\cos\theta}+\frac{\cos\theta}{1-\sin\theta}=2\sec\theta$$

I started with the left side and used the lcm to get...

$$\displaystyle \frac{1-\sin\theta-\sin\theta+\sin^2\theta+\cos^2\theta}{(1-\sin\theta)(\cos\theta)}$$

Then simplified to get...

$$\displaystyle \frac{2-2\sin\theta}{(1-\sin\theta)(\cos\theta)}$$

e^(i*pi) - you're fine up to here

and finally...

$$\displaystyle \frac{1-\sin\theta}{\cos\theta}$$

I obviously messed something up somewhere can anyone tell me where I went wrong?
$$\displaystyle \frac{2-2\sin\theta}{(1-\sin\theta)(\cos\theta)} = \frac{2(1-\sin\theta)}{(1-\sin\theta)(\cos\theta)}$$

$$\displaystyle 1-sin\theta$$ will cancel leaving $$\displaystyle \frac{2}{cos\theta} = 2sec\theta$$

repete

#### repete

Oh! Awesome Thanks!