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avanturin [10]
3 years ago
10

Can someone write out the steps on how to verify this identity?

Mathematics
1 answer:
zhenek [66]3 years ago
3 0

Step-by-step explanation:

(csc θ − 1) / cot θ

Multiply top and bottom by the conjugate csc θ + 1.

(csc θ − 1) (csc θ + 1) / (cot θ (csc θ + 1))

Distribute.

(csc²θ − 1) / (cot θ (csc θ + 1))

Use Pythagorean identity.

cot²θ / (cot θ (csc θ + 1))

Divide.

cot θ /  (csc θ + 1)

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A carpenter is building a rectangular room with a fixed perimeter of 300 ft. what dimensions would yield the maximum​ area?
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Perimeter = 2(Length) + 2(Width)

300 = 2L + 2W → 150 = L + W → 150 - L = W

Area = Length · Width

A_{max} = L(150 - L) → A_{max} = 150L - L²

There are 2 different methods for solving (depending on which math course you are taking).

<u>Calculus</u>: find the derivative, set it equal to zero, and solve for L.

A_{max} = 150L - L² → 0 = 150 - 2L → 2L = 150 → L = 75

<u>Algebra</u>: find the vertex.

A_{max} = - L² + 150L → L = -b/2a → L = -150/2(-1) → L = 75

Once you solve for L, plug it into the Perimeter equation to solve for W:

150 - L = W → 150 - 75 = W → W = 75

Answer: 75ft x 75ft


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So use the <span>Pythagorean Theorem. A^2 + B^2 = C^2    10^2 +12^2 = 15.6 hope this helps.

</span>
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