QuestionJuly 16, 2025

Find an equivalent expression for 3csc(x-(pi )/(2)) using the cofunction identities. 3csc(x-(pi )/(2))=square (Simplify your answer.)

Find an equivalent expression for 3csc(x-(pi )/(2)) using the cofunction identities. 3csc(x-(pi )/(2))=square (Simplify your answer.)
Find an equivalent expression for 3csc(x-(pi )/(2)) using the cofunction identities.
3csc(x-(pi )/(2))=square  (Simplify your answer.)

Solution
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Answer

( 3 \sec(x) ) Explanation 1. Apply Cofunction Identity The cofunction identity for cosecant is \csc\left(\frac{\pi}{2} - \theta\right) = \sec(\theta). Therefore, \csc\left(x - \frac{\pi}{2}\right) = \sec(x). 2. Simplify the Expression Multiply by 3: 3 \csc\left(x - \frac{\pi}{2}\right) = 3 \sec(x).

Explanation

1. Apply Cofunction Identity<br /> The cofunction identity for cosecant is $\csc\left(\frac{\pi}{2} - \theta\right) = \sec(\theta)$. Therefore, $\csc\left(x - \frac{\pi}{2}\right) = \sec(x)$.<br />2. Simplify the Expression<br /> Multiply by 3: $3 \csc\left(x - \frac{\pi}{2}\right) = 3 \sec(x)$.
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