If \(\sec ^2 \theta+\tan ^2 \theta=2\), find \(\theta\)
A. 45 \(^{\circ}\)
B. \(60^{\circ}\)
C. \(35^{\circ}\)
D. \(90^{\circ}\)
Correct Answer: C
Explanation
\begin{array}{l}
\sec ^2 \theta+\tan ^2 \theta=2 \\
1+\tan ^2 \theta=\sec ^2 \theta \\
\text { Then, } \\
1+\tan ^2 \theta+\tan ^2 \theta=2 \\
1+2 \tan ^2 \theta=2 \\
2 \tan ^2 \theta=2-1=1 \\
\tan ^2 \theta=1 / 2 \\
\tan \theta=\sqrt{\frac{1}{2}}=\frac{1}{\sqrt{2}}=0.7071 \\
\theta=\tan ^{-1} 0.7071 \\
=35.26^{\circ}
\end{array}