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Trigonometry Examples
Step 1
Step 1.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 1.2
Remove parentheses.
Step 1.3
The LCM of one and any expression is the expression.
Step 2
Step 2.1
Multiply each term in by .
Step 2.2
Simplify the left side.
Step 2.2.1
Cancel the common factor of .
Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Rewrite the expression.
Step 2.3
Simplify the right side.
Step 2.3.1
Apply the distributive property.
Step 2.3.2
Simplify the expression.
Step 2.3.2.1
Move to the left of .
Step 2.3.2.2
Reorder factors in .
Step 3
Step 3.1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 3.2
Multiply by by adding the exponents.
Step 3.2.1
Move .
Step 3.2.2
Multiply by .
Step 3.3
Subtract from both sides of the equation.
Step 3.4
Add to both sides of the equation.
Step 3.5
Use the quadratic formula to find the solutions.
Step 3.6
Substitute the values , , and into the quadratic formula and solve for .
Step 3.7
Simplify.
Step 3.7.1
Simplify the numerator.
Step 3.7.1.1
Add parentheses.
Step 3.7.1.2
Let . Substitute for all occurrences of .
Step 3.7.1.2.1
Apply the product rule to .
Step 3.7.1.2.2
Raise to the power of .
Step 3.7.1.3
Factor out of .
Step 3.7.1.3.1
Factor out of .
Step 3.7.1.3.2
Factor out of .
Step 3.7.1.3.3
Factor out of .
Step 3.7.1.4
Replace all occurrences of with .
Step 3.7.1.5
Simplify each term.
Step 3.7.1.5.1
Apply the distributive property.
Step 3.7.1.5.2
Move to the left of .
Step 3.7.1.5.3
Multiply by .
Step 3.7.1.5.4
Apply the distributive property.
Step 3.7.1.5.5
Multiply by .
Step 3.7.1.5.6
Multiply by .
Step 3.7.1.6
Rewrite as .
Step 3.7.1.6.1
Rewrite as .
Step 3.7.1.6.2
Rewrite as .
Step 3.7.1.7
Pull terms out from under the radical.
Step 3.7.1.8
Apply the product rule to .
Step 3.7.1.9
Raise to the power of .
Step 3.7.2
Simplify .
Step 3.8
The final answer is the combination of both solutions.