Trigonometry Examples

Verify the Identity tan(a)+cot(a)=sec(a)*csc(a)
Step 1
Start on the left side.
Step 2
Convert to sines and cosines.
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Step 2.1
Write in sines and cosines using the quotient identity.
Step 2.2
Write in sines and cosines using the quotient identity.
Step 3
Add fractions.
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Step 3.1
To write as a fraction with a common denominator, multiply by .
Step 3.2
To write as a fraction with a common denominator, multiply by .
Step 3.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 3.3.1
Multiply by .
Step 3.3.2
Multiply by .
Step 3.3.3
Reorder the factors of .
Step 3.4
Combine the numerators over the common denominator.
Step 4
Simplify each term.
Step 5
Apply pythagorean identity.
Step 6
Rewrite as .
Step 7
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity