Step-by-step explanation:
a)
[tex]\sin^{2}x + \cos^{2}x = 1[/tex]
Dividing both sides by sin^2x, we get
[tex]1 + \frac{\cos^{2}x }{ \sin^{2}x} = \frac{1}{\sin^{2}x } [/tex]
The 2nd term on the LHS is simply cot^2x and the RHS is simply csc^2x
[tex]1 + \cot^{2}x = \csc^{2}x[/tex]
b)
[tex]2 \sin x = 1[/tex]
[tex] \sin x = \frac{1}{2} [/tex]
[tex]x = \sin^{ - 1} (\frac{1}{2}) = \frac{\pi}{6} [/tex]
You can also graph it to arrive at the solution.
