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Trigonometry Examples
Step 1
Step 1.1
Simplify each term.
Step 1.1.1
Apply the product rule to .
Step 1.1.2
Raise to the power of .
Step 1.1.3
Simplify the numerator.
Step 1.1.3.1
Apply the sine double-angle identity.
Step 1.1.3.2
Multiply by .
Step 1.1.4
Cancel the common factor of .
Step 1.1.4.1
Cancel the common factor.
Step 1.1.4.2
Divide by .
Step 1.1.5
Multiply by .
Step 2
Substitute for .
Step 3
Add to both sides of the equation.
Step 4
Use the quadratic formula to find the solutions.
Step 5
Substitute the values , , and into the quadratic formula and solve for .
Step 6
Step 6.1
Simplify the numerator.
Step 6.1.1
Raise to the power of .
Step 6.1.2
Multiply .
Step 6.1.2.1
Multiply by .
Step 6.1.2.2
Multiply by .
Step 6.1.3
Subtract from .
Step 6.1.4
Rewrite as .
Step 6.1.5
Rewrite as .
Step 6.1.6
Rewrite as .
Step 6.1.7
Rewrite as .
Step 6.1.7.1
Factor out of .
Step 6.1.7.2
Rewrite as .
Step 6.1.8
Pull terms out from under the radical.
Step 6.1.9
Move to the left of .
Step 6.2
Multiply by .
Step 6.3
Simplify .
Step 7
The final answer is the combination of both solutions.
Step 8
Substitute for .
Step 9
Set up each of the solutions to solve for .
Step 10
Step 10.1
Take the inverse sine of both sides of the equation to extract from inside the sine.
Step 10.2
The inverse sine of is undefined.
Undefined
Undefined
Step 11
Step 11.1
Take the inverse sine of both sides of the equation to extract from inside the sine.
Step 11.2
The inverse sine of is undefined.
Undefined
Undefined
Step 12
List all of the solutions.
No solution