Rewrite cot(cos^-1 6u) as an algebraic expression in u.

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madeleinejames20 · Accepted Answer

To rewrite cot(cos−1(6u)) as an algebraic expression in u, we can use the trigonometric identities to simplify the expression.Let&#039;s begin by considering the expression cos−1(6u). The inverse cosine function returns an angle whose cosine is equal to 6u. We can denote this angle as θ, such that cos(θ)=6u.Now, we can rewrite cot(cos−1(6u)) using the definition of the cotangent function:cot(θ)=cos(θ)sin(θ)Substituting θ with cos−1(6u), we have:cot(cos−1(6u))=cos(cos−1(6u))sin(cos−1(6u))Using the identity sin2(θ)+cos2(θ)=1, we can find the value of sin(cos−1(6u)) by using the Pythagorean identity:sin(cos−1(6u))=1−cos2(cos−1(6u))Since cos(cos−1(6u))=6u, we can substitute this back into the expression:sin(cos−1(6u))=1−(6u)2Now we have both cos(cos−1(6u)) and sin(cos−1(6u)) in terms of u. Substituting these values back into the expression, we get:cot(cos−1(6u))=6u1−(6u)2Therefore, the algebraic expression equivalent to cot(cos−1(6u)) is 6u1−(6u)2.

Rewrite cot(cos^-1 6u) as an algebraic expression in

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