Simplify cot(arcsin(-( square root of 5)/4))

Math
Draw a triangle in the plane with vertices , , and the origin. Then is the angle between the positive x-axis and the ray beginning at the origin and passing through . Therefore, is .
Multiply the numerator by the reciprocal of the denominator.
One to any power is one.
Use the power rule to distribute the exponent.
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Apply the product rule to .
Apply the product rule to .
Multiply by by adding the exponents.
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Move .
Multiply by .
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Raise to the power of .
Use the power rule to combine exponents.
Add and .
Raise to the power of .
Rewrite as .
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Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Evaluate the exponent.
Raise to the power of .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Rewrite as .
Simplify the denominator.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Simplify terms.
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Cancel the common factor of .
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Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Move to the left of .
Multiply by .
Combine and simplify the denominator.
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
Tap for more steps…
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Evaluate the exponent.
Simplify the numerator.
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Combine using the product rule for radicals.
Multiply by .
Move the negative in front of the fraction.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Simplify cot(arcsin(-( square root of 5)/4))

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