Trigonometry Examples

Simplify sin(225)^2-cos(300)^2
Step 1
Simplify each term.
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Step 1.1
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant.
Step 1.2
The exact value of is .
Step 1.3
Use the power rule to distribute the exponent.
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Step 1.3.1
Apply the product rule to .
Step 1.3.2
Apply the product rule to .
Step 1.4
Raise to the power of .
Step 1.5
Multiply by .
Step 1.6
Rewrite as .
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Step 1.6.1
Use to rewrite as .
Step 1.6.2
Apply the power rule and multiply exponents, .
Step 1.6.3
Combine and .
Step 1.6.4
Cancel the common factor of .
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Step 1.6.4.1
Cancel the common factor.
Step 1.6.4.2
Rewrite the expression.
Step 1.6.5
Evaluate the exponent.
Step 1.7
Raise to the power of .
Step 1.8
Cancel the common factor of and .
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Step 1.8.1
Factor out of .
Step 1.8.2
Cancel the common factors.
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Step 1.8.2.1
Factor out of .
Step 1.8.2.2
Cancel the common factor.
Step 1.8.2.3
Rewrite the expression.
Step 1.9
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
Step 1.10
The exact value of is .
Step 1.11
Apply the product rule to .
Step 1.12
One to any power is one.
Step 1.13
Raise to the power of .
Step 2
To write as a fraction with a common denominator, multiply by .
Step 3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 3.1
Multiply by .
Step 3.2
Multiply by .
Step 4
Combine the numerators over the common denominator.
Step 5
Subtract from .
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: