Trigonometry Examples

Verify the Identity cos(pi-x)=-cos(x)
Step 1
Start on the left side.
Step 2
Apply the difference of angles identity .
Step 3
Simplify the expression.
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Step 3.1
Simplify each term.
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Step 3.1.1
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.
Step 3.1.2
The exact value of is .
Step 3.1.3
Multiply by .
Step 3.1.4
Rewrite as .
Step 3.1.5
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
Step 3.1.6
The exact value of is .
Step 3.1.7
Multiply by .
Step 3.2
Add and .
Step 4
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity