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Question Video: Finding Equivalent Expressions Using the Cofunction Identity for the Tangent and Cotangent Mathematics

Which of the following is equivalent to 3 cot (43°)? [A] 3 tan (47°) [B] 3 tan (133°) [C] −3 tan (47°) [D] 6 tan (43°) [E] −6 tan (133°)

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Video Transcript

Which of the following is equivalent to three cot 43 degrees? (A) Three tan of 47 degrees. (B) Three tan of 133 degrees. (C) Negative three tan of 47 degrees. (D) Six tan of 43 degrees. Or (E) negative six tan of 133 degrees.

Based on the options we have, we can see that we’re trying to take this cotangent value and rewrite it in the form of a tangent value. Recall the cofunction identity that tells us that the tan of 90 degrees minus 𝜃 equals the cot of 𝜃. In this case, we can let 43 degrees equal 𝜃. Therefore, tan of 90 degrees minus 43 degrees equals the cot of 43 degrees. tan of 47 degrees equals the cot of 43 degrees, which means that three times the tan of 47 degrees is equal to three times the cot of 43 degrees. This is expressed in option (A). Three tan of 47 degrees is equal to three cot of 43 degrees.

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