Trigonometry Examples

Simplify cos(arctan(x))
Step 1
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 .
Step 2
Multiply by .
Step 3
Combine and simplify the denominator.
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Step 3.1
Multiply by .
Step 3.2
Raise to the power of .
Step 3.3
Raise to the power of .
Step 3.4
Use the power rule to combine exponents.
Step 3.5
Add and .
Step 3.6
Rewrite as .
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Step 3.6.1
Use to rewrite as .
Step 3.6.2
Apply the power rule and multiply exponents, .
Step 3.6.3
Combine and .
Step 3.6.4
Cancel the common factor of .
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Step 3.6.4.1
Cancel the common factor.
Step 3.6.4.2
Rewrite the expression.
Step 3.6.5
Simplify.