Chapter 12.2, Problem 7OE

To determine

Use the cofunction identities to find the measure of the acute angle $\theta$ .

  $\sec \theta =\csc 15°$

Answer to Problem 7OE

  $\theta =75°$

Explanation of Solution

Given:

  $\sec \theta =\csc 15°$

Formula Used:

  $\csc \theta =\sec \left(90°-\theta \right)$

Calculation:

  $\begin{array}{l}\sec \theta =\csc 15°\\ \Rightarrow \sec \theta =\sec \left(90°-15°\right)\mathrm{...........}[\csc \theta =\sec \left(90°-\theta \right)]\\ \Rightarrow \sec \theta =\sec 75°\\ \Rightarrow \theta =75°\mathrm{.................................}[\sec x=\sec y\iff x=y\text{ in first quadrant]}\end{array}$