Question

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Answer 1

For this case you must take into account the following:
1) Trigonometric properties.
2) trigonometric equations
3) Division of fractions.
Answer:
cotx = root (15) / 7
See attached image.

Answer 2

Answer:
cot θ = √15 / 7

Step-by-step explanation:
csc θ = 1 / sin θ
In a right angled triangle, sin θ = opposite / hypotenuse
This means that:
csc θ = hypotenuse / opposite = 8 / 7
So, we have:
opposite = 7 units and hypotenuse = 8 units
We will use the Pythagorean theorem to get the adjacent side as follows:
(hypotenuse)^2 = (opposite)^2 + (adjacent)^2
(8)^2 = (7)^2 + (adjacent)^2
(adjacent)^2 = 15
adjacent = √15 units

Now, we want to get the value of cot θ.
We know that:
cot θ = 1 / tan θ
Since tan θ = opposite / adjacent
Therefore:
cot θ = adjacent / opposite = √15 / 7

Hope this helps :)