Question

50 POINTS

Answer 1

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Answer 2

Step-by-step explanation:

a)

$\sin^{2}x + \cos^{2}x = 1$

Dividing both sides by sin^2x, we get

$1 + \frac{\cos^{2}x }{ \sin^{2}x} = \frac{1}{\sin^{2}x }$

The 2nd term on the LHS is simply cot^2x and the RHS is simply csc^2x

$1 + \cot^{2}x = \csc^{2}x$

b)

$2 \sin x = 1$

$\sin x = \frac{1}{2}$

$x = \sin^{ - 1} (\frac{1}{2}) = \frac{\pi}{6}$

You can also graph it to arrive at the solution.