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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
Apply the product rule to .
Step 3.3.1.2
Raise to the power of .
Step 4
Step 4.1
Multiply both sides by .
Step 4.2
Simplify.
Step 4.2.1
Simplify the left side.
Step 4.2.1.1
Cancel the common factor of .
Step 4.2.1.1.1
Cancel the common factor.
Step 4.2.1.1.2
Rewrite the expression.
Step 4.2.2
Simplify the right side.
Step 4.2.2.1
Cancel the common factor of .
Step 4.2.2.1.1
Factor out of .
Step 4.2.2.1.2
Cancel the common factor.
Step 4.2.2.1.3
Rewrite the expression.
Step 4.3
Solve for .
Step 4.3.1
Multiply both sides by .
Step 4.3.2
Simplify.
Step 4.3.2.1
Simplify the left side.
Step 4.3.2.1.1
Simplify .
Step 4.3.2.1.1.1
Simplify by multiplying through.
Step 4.3.2.1.1.1.1
Apply the distributive property.
Step 4.3.2.1.1.1.2
Reorder.
Step 4.3.2.1.1.1.2.1
Move to the left of .
Step 4.3.2.1.1.1.2.2
Move to the left of .
Step 4.3.2.1.1.2
Multiply by .
Step 4.3.2.2
Simplify the right side.
Step 4.3.2.2.1
Cancel the common factor of .
Step 4.3.2.2.1.1
Cancel the common factor.
Step 4.3.2.2.1.2
Rewrite the expression.
Step 4.3.3
Solve for .
Step 4.3.3.1
Simplify .
Step 4.3.3.1.1
Rewrite.
Step 4.3.3.1.2
Rewrite as .
Step 4.3.3.1.3
Expand using the FOIL Method.
Step 4.3.3.1.3.1
Apply the distributive property.
Step 4.3.3.1.3.2
Apply the distributive property.
Step 4.3.3.1.3.3
Apply the distributive property.
Step 4.3.3.1.4
Simplify and combine like terms.
Step 4.3.3.1.4.1
Simplify each term.
Step 4.3.3.1.4.1.1
Multiply by .
Step 4.3.3.1.4.1.2
Multiply by .
Step 4.3.3.1.4.2
Add and .
Step 4.3.3.1.4.2.1
Reorder and .
Step 4.3.3.1.4.2.2
Add and .
Step 4.3.3.2
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 4.3.3.3
Move all terms containing to the left side of the equation.
Step 4.3.3.3.1
Subtract from both sides of the equation.
Step 4.3.3.3.2
Subtract from .
Step 4.3.3.4
Move all terms to the left side of the equation and simplify.
Step 4.3.3.4.1
Subtract from both sides of the equation.
Step 4.3.3.4.2
Subtract from .
Step 4.3.3.5
Use the quadratic formula to find the solutions.
Step 4.3.3.6
Substitute the values , , and into the quadratic formula and solve for .
Step 4.3.3.7
Simplify.
Step 4.3.3.7.1
Simplify the numerator.
Step 4.3.3.7.1.1
Rewrite as .
Step 4.3.3.7.1.2
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 4.3.3.7.1.3
Simplify.
Step 4.3.3.7.1.3.1
Add and .
Step 4.3.3.7.1.3.2
Multiply by .
Step 4.3.3.7.1.4
Subtract from .
Step 4.3.3.7.1.5
Combine exponents.
Step 4.3.3.7.1.5.1
Multiply by .
Step 4.3.3.7.1.5.2
Multiply by .
Step 4.3.3.7.1.6
Rewrite as .
Step 4.3.3.7.1.7
Pull terms out from under the radical, assuming positive real numbers.
Step 4.3.3.7.1.8
plus or minus is .
Step 4.3.3.7.2
Multiply by .
Step 4.3.3.7.3
Cancel the common factor of .
Step 4.3.3.7.3.1
Cancel the common factor.
Step 4.3.3.7.3.2
Divide by .
Step 4.3.3.8
The final answer is the combination of both solutions.
Double roots
Double roots
Double roots
Double roots