I've got a take home test and only 3 hours left to do it, I'm not creative at all when it comes to trig identities, please prove this one

tan theta + cot theta = (sec theta)(csc theta)

also,

"find sin(theta+phi)

cos theta = -1/5 and sin phi = 3/5, with both angles in quadrant 2!

I've got a take home test and only 3 hours left to do it, I'm not creative at all when it comes to trig identities, please prove this one

[quote]tan{\theta} + cot{\theta} = (sec{\theta})(csc{\theta})

Rewrite as:

\frac{sin{\theta}}{cos{\theta}}+\frac{cos{\theta}} {sin{\theta}}

Cross-multiply:

\frac{\overbrace{sin^{2}{\theta}+cos^{2}{\theta}}^ {\text{this equals 1}}}{cos{\theta}sin{\theta}}

\frac{1}{cos{\theta}}\cdot\frac{1}{sin{\theta}}=se c{\theta}csc{\theta}

"find sin(theta+phi)

cos theta = -1/5 and sin phi = 3/5, with both angles in quadrant 2!

{\theta}=cos^{-1}(\frac{-1}{5})=sin^{-1}(\frac{1}{5})+\frac{\pi}{2}\approx{1.772154}, \;\ about \;\ 101.54 \;\ degrees.

{\phi}=sin^{-1}(\frac{3}{5})\approx{0.6425011}, \;\ about \;\ 36.87 \;\ degrees.

Use these to find sin({\theta}+{\phi})

Remember, you're in the 2nd quadrant.