Simplify arcsec(2/( square root of 3))

Problem

arcsec(2/√(,3))

Solution

1. Identify the definition of the inverse secant function, where y=arcsec(x) implies sec(y)=x for y in the range [0,π/2)∪(π/2,π]

2. Rewrite the expression as an equation involving the secant function.

sec(y)=2/√(,3)

3. Convert the secant function to the cosine function using the reciprocal identity cos(y)=1/sec(y)

cos(y)=√(,3)/2

4. Determine the angle y in the interval [0,π] that satisfies the cosine equation.

y=π/6

Final Answer

arcsec(2/√(,3))=π/6

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