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Trigonometry Examples
Step 1
Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 2
To remove the radical on the left side of the equation, square both sides of the equation.
Step 3
Step 3.1
Use to rewrite as .
Step 3.2
Simplify the left side.
Step 3.2.1
Simplify .
Step 3.2.1.1
Multiply the exponents in .
Step 3.2.1.1.1
Apply the power rule and multiply exponents, .
Step 3.2.1.1.2
Cancel the common factor of .
Step 3.2.1.1.2.1
Cancel the common factor.
Step 3.2.1.1.2.2
Rewrite the expression.
Step 3.2.1.2
Simplify.
Step 3.3
Simplify the right side.
Step 3.3.1
Simplify .
Step 3.3.1.1
Write the expression using exponents.
Step 3.3.1.1.1
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 3.3.1.1.2
Rewrite as .
Step 3.3.1.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 3.3.1.3
Simplify by cancelling exponent with radical.
Step 3.3.1.3.1
Apply the product rule to .
Step 3.3.1.3.2
Raise to the power of .
Step 3.3.1.3.3
Rewrite as .
Step 3.3.1.3.3.1
Use to rewrite as .
Step 3.3.1.3.3.2
Apply the power rule and multiply exponents, .
Step 3.3.1.3.3.3
Combine and .
Step 3.3.1.3.3.4
Cancel the common factor of .
Step 3.3.1.3.3.4.1
Cancel the common factor.
Step 3.3.1.3.3.4.2
Rewrite the expression.
Step 3.3.1.3.3.5
Simplify.
Step 3.3.1.4
Expand using the FOIL Method.
Step 3.3.1.4.1
Apply the distributive property.
Step 3.3.1.4.2
Apply the distributive property.
Step 3.3.1.4.3
Apply the distributive property.
Step 3.3.1.5
Simplify and combine like terms.
Step 3.3.1.5.1
Simplify each term.
Step 3.3.1.5.1.1
Multiply by .
Step 3.3.1.5.1.2
Multiply by .
Step 3.3.1.5.1.3
Multiply by .
Step 3.3.1.5.1.4
Rewrite using the commutative property of multiplication.
Step 3.3.1.5.1.5
Multiply by by adding the exponents.
Step 3.3.1.5.1.5.1
Move .
Step 3.3.1.5.1.5.2
Multiply by .
Step 3.3.1.5.2
Add and .
Step 3.3.1.5.3
Add and .
Step 3.3.1.6
Apply the distributive property.
Step 3.3.1.7
Multiply.
Step 3.3.1.7.1
Multiply by .
Step 3.3.1.7.2
Multiply by .
Step 4
Step 4.1
Move all terms containing to the left side of the equation.
Step 4.1.1
Add to both sides of the equation.
Step 4.1.2
Combine the opposite terms in .
Step 4.1.2.1
Add and .
Step 4.1.2.2
Add and .
Step 4.2
Since , the equation will always be true for any value of .
All real numbers
All real numbers
Step 5
The result can be shown in multiple forms.
All real numbers
Interval Notation: