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Trigonometry Examples
Step 1
Square both sides of the equation.
Step 2
Step 2.1
Rewrite as .
Step 2.2
Expand using the FOIL Method.
Step 2.2.1
Apply the distributive property.
Step 2.2.2
Apply the distributive property.
Step 2.2.3
Apply the distributive property.
Step 2.3
Simplify and combine like terms.
Step 2.3.1
Simplify each term.
Step 2.3.1.1
Multiply .
Step 2.3.1.1.1
Raise to the power of .
Step 2.3.1.1.2
Raise to the power of .
Step 2.3.1.1.3
Use the power rule to combine exponents.
Step 2.3.1.1.4
Add and .
Step 2.3.1.1.5
Raise to the power of .
Step 2.3.1.1.6
Raise to the power of .
Step 2.3.1.1.7
Use the power rule to combine exponents.
Step 2.3.1.1.8
Add and .
Step 2.3.1.2
Rewrite as .
Step 2.3.1.2.1
Use to rewrite as .
Step 2.3.1.2.2
Apply the power rule and multiply exponents, .
Step 2.3.1.2.3
Combine and .
Step 2.3.1.2.4
Cancel the common factor of .
Step 2.3.1.2.4.1
Cancel the common factor.
Step 2.3.1.2.4.2
Rewrite the expression.
Step 2.3.1.2.5
Evaluate the exponent.
Step 2.3.1.3
Multiply .
Step 2.3.1.3.1
Combine using the product rule for radicals.
Step 2.3.1.3.2
Multiply by .
Step 2.3.1.4
Rewrite as .
Step 2.3.1.4.1
Factor out of .
Step 2.3.1.4.2
Rewrite as .
Step 2.3.1.5
Pull terms out from under the radical.
Step 2.3.1.6
Multiply .
Step 2.3.1.6.1
Combine using the product rule for radicals.
Step 2.3.1.6.2
Multiply by .
Step 2.3.1.7
Rewrite as .
Step 2.3.1.7.1
Factor out of .
Step 2.3.1.7.2
Rewrite as .
Step 2.3.1.8
Pull terms out from under the radical.
Step 2.3.1.9
Multiply .
Step 2.3.1.9.1
Raise to the power of .
Step 2.3.1.9.2
Raise to the power of .
Step 2.3.1.9.3
Use the power rule to combine exponents.
Step 2.3.1.9.4
Add and .
Step 2.3.1.9.5
Raise to the power of .
Step 2.3.1.9.6
Raise to the power of .
Step 2.3.1.9.7
Use the power rule to combine exponents.
Step 2.3.1.9.8
Add and .
Step 2.3.1.10
Rewrite as .
Step 2.3.1.10.1
Use to rewrite as .
Step 2.3.1.10.2
Apply the power rule and multiply exponents, .
Step 2.3.1.10.3
Combine and .
Step 2.3.1.10.4
Cancel the common factor of .
Step 2.3.1.10.4.1
Cancel the common factor.
Step 2.3.1.10.4.2
Rewrite the expression.
Step 2.3.1.10.5
Evaluate the exponent.
Step 2.3.2
Reorder the factors of .
Step 2.3.3
Add and .
Step 3
Step 3.1
Add and .
Step 3.2
Rewrite using the commutative property of multiplication.
Step 3.3
Use the power rule to distribute the exponent.
Step 3.3.1
Apply the product rule to .
Step 3.3.2
Apply the product rule to .
Step 3.3.3
Apply the product rule to .
Step 3.4
Raise to the power of .
Step 4
Subtract from both sides of the equation.
Step 5
Replace the with based on the identity.
Step 6
Step 6.1
Apply the distributive property.
Step 6.2
Multiply by .
Step 6.3
Multiply by .
Step 7
Add and .
Step 8
Step 8.1
Simplify each term.
Step 8.1.1
Apply the product rule to .
Step 8.1.2
Rewrite as .
Step 8.1.3
Move to the left of .
Step 8.1.4
Rewrite as .
Step 8.1.5
Multiply by .
Step 8.2
Reorder factors in .