How do I simplify tan$\theta$ cos$\theta$ ?
Why is this so hard to do? What pieces of information should I know before doing these?
Can someone just tell me were am I going wrong? I have 5 days to master this before my SAT Practice.
I would brush up on 'basics' but i don't even know how this related to anything ive learnt in trig before…I literally google every identity, am i supposed to remember or somehow derive them??
Best Answer
Notice first that the $\tan$ function is defined on $D:=\Bbb R\setminus\{\frac\pi2+k\pi,\; k\in\Bbb Z\}$ and that $\tan\theta=\frac{\sin\theta}{\cos\theta}$ so
$$\tan\theta\cos\theta=\sin\theta,\quad\forall\theta\in D$$ and be careful the trap is to give a wrong domain.