Any help would be appreciated for these problems. Thanks in advance
csc(squared)x-4=0
sec x/2 = cos x/2
2sin(squared)x-cosx=1
3sec(squared)x+4cos(squared)x=7
1) $\displaystyle \csc^2x-4=0$
$\displaystyle \csc^2 x=4$
$\displaystyle \csc x=\pm 2$
For what value of x does $\displaystyle \csc x$ has $\displaystyle 2$ or $\displaystyle -2$ as its value?
2) $\displaystyle \sec x/2=\cos x/2$
$\displaystyle \frac 1{\cos x/2}=\cos x/2$
$\displaystyle \cos^2 x/2=1$
Can you proceed further?
3)$\displaystyle 2\sin^2-\cos x=1$
$\displaystyle 2(1-\cos^2 x)-\cos x=1$
$\displaystyle 2-2\cos^2 x-\cos x=1$
$\displaystyle 2\cos^2 x+\cos x-1=0$
Solve it...
4)Try to do this yourself as number 3 or else i will give further hints...