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Answer
Solution
Given the equation
we start by isolating
. Add
to both sides and then divide by
:
Next, recall the Pythagorean identity:
Substitute
:
The cosecant squared is defined as the reciprocal of
:
Thus, the value of
is
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Extra Insights
To solve the equation
, we first isolate
:
Next, we need to find
. We can use the identity relating cosecant and cosine:
To find
, we can use the Pythagorean identity:
Substituting
:
Calculating
:
Now, subtract
from both sides:
To express 1 with a common denominator:
Thus:
Now, we substitute
into the cosecant formula:
Therefore, the value of
is