What is sin^{-5}(sqrt(((1+x^2))/2)) ?

The solution to sin^{-5}(sqrt(((1+x^2))/2)) is csc^5(sqrt((x^2+1)/2))

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simplify sin^{-5}(sqrt(((1+x^2))/2))

simplify

sin^{- 5} (\frac{( 1 + x ^{2} )}{2})

csc^{5} (\frac{x ^{2} + 1}{2})

Solution steps

sin^{- 5} (\frac{1 + x ^{2}}{2})

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

sin^{- 5} (\frac{1 + x ^{2}}{2}) = \frac{1}{sin ^{5} ( \frac{1 + x ^{2}}{2} )}

= \frac{1}{sin ^{5} ( \frac{1 + x ^{2}}{2} )}

Use the basic trigonometric identity:

\frac{1}{sin ( x )} = csc (x)

= csc^{5} (\frac{x ^{2} + 1}{2})

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What is sin^{-5}(sqrt(((1+x^2))/2)) ?
The solution to sin^{-5}(sqrt(((1+x^2))/2)) is csc^5(sqrt((x^2+1)/2))