Verify trig identity: 1/(tanx-secx) + 1/(tanx+secx) = -2tanx

[HannahBanana4011]

I've completed about 12 similar homework problems, but for some reason, I can't figure out how to verify this one. Any help would be greatly appreciated!!

[1/(tanx-secx)]+[1/(tanx+secx)] = -2tanx

 

[galactus]

Re: Verifying trig identites

Cross multiply as you would when adding any fraction, then simplify.

\(\displaystyle \frac{1}{tan(x)-sec(x)}+\frac{1}{tan(x)+sec(x)}\)

=\(\displaystyle \frac{tan(x)+sec(x)+tan(x)-sec(x)}{tan^{2}(x)-sec^{2}(x)}\)

Now, simplify. See it?. Remember the identity \(\displaystyle tan^{2}(x)-sec^{2}(x)=-1\)