AP EAMCET · Maths · Trigonometric Equations
If \(\theta\) is in the interval \(\left(0, \frac{\pi}{2}\right)\) satisfying the equation \(\cos 2 \theta \cdot \sec ^4 \theta+\sec ^2 \theta=0\), then \(\sin ^2 \theta=\)
- A \(\frac{1}{3}\)
- B \(\frac{3}{4}\)
- C \(\frac{1}{2}\)
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{2}{3}\)
Step-by-step Solution
Detailed explanation
\begin{array}{lrl}\text {Given, } \cos 2 \theta \cdot \sec ^4 \theta+\sec ^2 \theta=0, \theta \in(0, \pi / 2) \\ \Rightarrow & \left(1-\tan ^2 \theta\right) \sec ^2 \theta+\sec ^2 \theta=0 \\ \Rightarrow & \sec ^2 \theta\left[1-\tan ^2 \theta+1\right]=0 \\ \Rightarrow & \tan ^2…
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