Math

QuestionFind the exact value of cot(π2θ)\cot \left(\frac{\pi}{2}-\theta\right) if tanθ=7\tan \theta=7.

Studdy Solution

STEP 1

Assumptions1. The tangent of theta is given as7, i.e., tanθ=7\tan \theta=7. . We need to find the exact value of cot(πθ)\cot \left(\frac{\pi}{}-\theta\right).
3. We will use the Complementary Angle Theorem, which states that tan(πθ)=cotθ\tan(\frac{\pi}{} - \theta) = \cot \theta.

STEP 2

We can start by applying the Complementary Angle Theorem to the expression cot(π2θ)\cot \left(\frac{\pi}{2}-\theta\right).
cot(π2θ)=tanθ\cot \left(\frac{\pi}{2}-\theta\right) = \tan \theta

STEP 3

Now, we can substitute the given value of tanθ=7\tan \theta =7 into the equation.
cot(π2θ)=7\cot \left(\frac{\pi}{2}-\theta\right) =7So, the exact value of cot(π2θ)\cot \left(\frac{\pi}{2}-\theta\right) is7.

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