Trigonometry Examples

Start on the left side.
Convert to sines and cosines.
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Write in sines and cosines using the quotient identity.
Write in sines and cosines using the quotient identity.
Add fractions.
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To write as a fraction with a common denominator, multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Combine.
Reorder terms.
Combine the numerators over the common denominator.
Simplify each term.
Apply pythagorean identity.
Now consider the right side of the equation.
Convert to sines and cosines.
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Apply the reciprocal identity to .
Apply the reciprocal identity to .
Multiply and to get .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
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