## anonymous 5 years ago tan^4 h -1 I need to express this in terms of sin h and cos h and simplify. I typed it wrong earlier. Sorry.

1. anonymous

is it really$tan^4(h-1)$ because if so this is a silly problem as tan is just sine over cosine. perhaps $tan^4(h)-1$?

2. anonymous

I don't know. This is how the teacher typed it on her worksheet. Could you show me how to simplify tan^4(h)-1. Thanks

3. anonymous

$tan^4(h)-1=(tan^2-1)(tan^2+1)$ and $tan^2(h)+1=sec^2(h)$ $(tan^2(h)-1)sec^2(h)=\frac{tan^2(h)-1}{cos^2(h)}$ $=\frac{\frac{sin^2(h)}{cos^2(h)}-1}{cos^2(h)}$ $=\frac{sin^2(h)}{cos^4(h)}-\frac{1}{cos^2(h)}$ or if you prefer $\frac{sin^2(h)-cos^2(h)}{cos^4(h)}$