# Thread: 2 trig problems pls help...

1. ## 2 trig problems pls help...

1) show that cosec $\theta$/(cosec $\theta$-sin $\theta$)=sec^2 $\theta$

2) solve: sin3 $\theta$cos2 $\theta$=sin2 $\theta$cos3 $\theta$ for 0< $\theta$<2 $\pi$

2. Hello, snowball!

1) Show that: . $\frac{\csc\theta}{\csc\theta -\sin\theta} \:=\:\sec^2\!\theta$

On the left side, multiply top and bottom by $\sin\theta$

. . $\frac{\sin\theta(\csc\theta)}{\sin\theta(\csc\thet a-\sin\theta)} \:=\:\frac{1}{1-\sin^2\!\theta} \;=\;\frac{1}{\cos^2\!\theta} \;=\;\sec^2\!\theta$

2) Solve: . $\sin3\theta\cos2\theta \:=\:\sin2\theta \cos3\theta,\;\;\text{ for }0 \leq \theta < 2\pi$

$\text{We have: }\;\underbrace{\sin3\theta\cos2\theta - \sin2\theta\cos3\theta} \;=\;0$

. . . . . . . . . . . $\overbrace{\sin(3\theta-2\theta)} \;=\;0$

. . . . . . . . . . . . $\sin\theta \;=\;0$

Therefore:. $\theta \;=\;0.\:\pi$