## owlet one year ago I'm wrong. My solution is wrong I think. Please help me. Question below

1. owlet

My solution is also iincluded

2. owlet

question: Solve $$\sf csc^2 x -1 = 4 cos^2x$$

3. SolomonZelman

$$\large\color{black}{ \displaystyle \csc^2x-1=4\cos^2x }$$ $$\large\color{black}{ \displaystyle \cot^2x=4\cos^2x }$$ $$\large\color{black}{ \displaystyle \left[\cos^2x~/~\sin^2x\right]=4\cos^2x }$$ $$\large\color{black}{ \displaystyle 1/\sin^2x=4 }$$ $$\large\color{black}{ \displaystyle 1/\sin^2x=1/{~~}(^1/_4) }$$ $$\large\color{black}{ \displaystyle \sin^2x=1/4 }$$

4. SolomonZelman

this is what I would start off.

5. owlet

then take the square root right? so you'll also end up with sin x = positive/negative 1/2

6. owlet

oh i think i get it.. I'm missing sin x= 1/2 which is Pi/6 so my solution is really messy. I'll try to do it again. thanks!

7. owlet

and 5pi/6 i think

8. SolomonZelman

* sin(x) = ½ * or * sin(x) = - ½ *

9. ParthKohli

$\cos (x) = 0$

10. triciaal

|dw:1443623788259:dw|

11. owlet

i'll start all over again, and I'll check if I'll get it right again.