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Answer:
,
Explanation:2√2 sin(q) + 2 = 0
2√2 sin(q) = -2
sin(q) =

sin(q) =

Now, we know that:
sin (45) =

From the ASTC rule, we know that the sine function is negative in the third and fourth quadrant.
This means that:
either q = 90 + 45 = 135° which is equivalent to

or q = 270 + 45 = 315° which is equivalent to

Hope this helps :)
Y = ln {[sin(x)]^2}
use the chain rule
y' = 1 /[sin(x)]^2 * 2sin(x)*cos(x) = 2cos(x) / sin(x) = 2 cot(x)
Answer: 2 cot(x)