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QuestionExpress tan⁡(β+25∘)\tan \left(\beta+25^{\circ}\right) using its cofunction for acute angles.

Studdy Solution

STEP 1

Assumptions1. The function is tan⁡(β+25∘)\tan \left(\beta+25^{\circ}\right). All angles in which an unknown appears are acute angles3. The cofunction identity for tangent is tan⁡(θ)=cot⁡(90∘−θ)\tan(\theta) = \cot(90^{\circ} - \theta)

STEP 2

We want to write the function in terms of its cofunction. To do this, we can use the cofunction identity for tangent, which is tan⁡(θ)=cot⁡(90∘−θ)\tan(\theta) = \cot(90^{\circ} - \theta).

STEP 3

Now, we can substitute β+25∘\beta+25^{\circ} for θ\theta in the cofunction identity.
tan⁡(β+25∘)=cot⁡(90∘−(β+25∘))\tan \left(\beta+25^{\circ}\right) = \cot\left(90^{\circ} - (\beta+25^{\circ})\right)

STEP 4

implify the expression inside the parentheses on the right side of the equation.
tan⁡(β+25∘)=cot⁡(65∘−β)\tan \left(\beta+25^{\circ}\right) = \cot\left(65^{\circ} - \beta\right)So, the function tan⁡(β+25∘)\tan \left(\beta+25^{\circ}\right) can be written as cot⁡(65∘−β)\cot\left(65^{\circ} - \beta\right) in terms of its cofunction.

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