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Trigonometry Examples
Step 1
Rewrite the equation as .
Step 2
Step 2.1
Simplify each term.
Step 2.1.1
The exact value of is .
Step 2.1.1.1
Split into two angles where the values of the six trigonometric functions are known.
Step 2.1.1.2
Apply the difference of angles identity.
Step 2.1.1.3
The exact value of is .
Step 2.1.1.4
The exact value of is .
Step 2.1.1.5
The exact value of is .
Step 2.1.1.6
The exact value of is .
Step 2.1.1.7
Simplify .
Step 2.1.1.7.1
Simplify each term.
Step 2.1.1.7.1.1
Multiply .
Step 2.1.1.7.1.1.1
Multiply by .
Step 2.1.1.7.1.1.2
Combine using the product rule for radicals.
Step 2.1.1.7.1.1.3
Multiply by .
Step 2.1.1.7.1.1.4
Multiply by .
Step 2.1.1.7.1.2
Multiply .
Step 2.1.1.7.1.2.1
Multiply by .
Step 2.1.1.7.1.2.2
Multiply by .
Step 2.1.1.7.2
Combine the numerators over the common denominator.
Step 2.1.2
Cancel the common factor of .
Step 2.1.2.1
Cancel the common factor.
Step 2.1.2.2
Rewrite the expression.
Step 2.1.3
Expand using the FOIL Method.
Step 2.1.3.1
Apply the distributive property.
Step 2.1.3.2
Apply the distributive property.
Step 2.1.3.3
Apply the distributive property.
Step 2.1.4
Simplify each term.
Step 2.1.4.1
Move to the left of .
Step 2.1.4.2
Multiply by .
Step 3
Step 3.1
Subtract from both sides of the equation.
Step 3.2
Subtract from both sides of the equation.
Step 3.3
Add to both sides of the equation.
Step 3.4
Subtract from .
Step 4
Step 4.1
Factor out of .
Step 4.2
Factor out of .
Step 4.3
Factor out of .
Step 5
Step 5.1
Divide each term in by .
Step 5.2
Simplify the left side.
Step 5.2.1
Cancel the common factor of .
Step 5.2.1.1
Cancel the common factor.
Step 5.2.1.2
Divide by .
Step 5.3
Simplify the right side.
Step 5.3.1
Combine the numerators over the common denominator.
Step 5.3.2
Multiply by .
Step 5.3.3
Multiply by .
Step 5.3.4
Expand the denominator using the FOIL method.
Step 5.3.5
Simplify.
Step 5.3.6
Cancel the common factor of and .
Step 5.3.6.1
Factor out of .
Step 5.3.6.2
Cancel the common factors.
Step 5.3.6.2.1
Factor out of .
Step 5.3.6.2.2
Cancel the common factor.
Step 5.3.6.2.3
Rewrite the expression.
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: