Trigonometry Examples

Simplify cos(theta)^2-sin(theta)^2
Step 1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2
Expand using the FOIL Method.
Tap for more steps...
Step 2.1
Apply the distributive property.
Step 2.2
Apply the distributive property.
Step 2.3
Apply the distributive property.
Step 3
Simplify terms.
Tap for more steps...
Step 3.1
Combine the opposite terms in .
Tap for more steps...
Step 3.1.1
Reorder the factors in the terms and .
Step 3.1.2
Add and .
Step 3.1.3
Add and .
Step 3.2
Simplify each term.
Tap for more steps...
Step 3.2.1
Multiply .
Tap for more steps...
Step 3.2.1.1
Raise to the power of .
Step 3.2.1.2
Raise to the power of .
Step 3.2.1.3
Use the power rule to combine exponents.
Step 3.2.1.4
Add and .
Step 3.2.2
Rewrite using the commutative property of multiplication.
Step 3.2.3
Multiply .
Tap for more steps...
Step 3.2.3.1
Raise to the power of .
Step 3.2.3.2
Raise to the power of .
Step 3.2.3.3
Use the power rule to combine exponents.
Step 3.2.3.4
Add and .
Step 4
Apply the cosine double-angle identity.