5
QuizMultiple Choice

Trigonometric Sum Identities — Quiz

Question 5 • Precalculus

Which steps can be used to verify that tangent of open paren w plus pi close paren is equal to tangent of w ?

Answer
A
Rewrite tangent of open paren w plus pi close paren as tangent of w plus tangent of pi . Then simplify the expression using tangent of pi is equal to 1 .
B
Rewrite tangent of open paren w plus pi close paren using the tangent sum identity. Then simplify the resulting expression using tangent of pi is equal to 1 .
C
Rewrite tangent of open paren w plus pi close paren as tangent of w plus tangent of pi . Then simplify the expression using tangent of pi is equal to 0 .
D
Rewrite tangent of open paren w plus pi close paren using the tangent sum identity. Then simplify the resulting expression using tangent of pi is equal to 0 .

Explanation

Use the tangent sum identity: tan(w + π) = (tan w + tan π) / (1 − tan w tan π). Since tan π = 0, this becomes (tan w + 0) / (1 − 0) = tan w. So the correct step is to use the tangent sum identity and simplify using tan π = 0.

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