TS EAMCET · Maths · Trigonometric Ratios & Identities
If \((\sin \theta-\operatorname{cosec} \theta)^2+(\cos \theta+\sec \theta)^2=5\) and \(\theta\) lies in the third quadrant, then \((\sin \theta+\cos \theta)^3=\)
- A \(-2 \sqrt{2}\)
- B \(2 \sqrt{2}\)
- C \(4\)
- D \(-4\)
Answer & Solution
Correct Answer
(A) \(-2 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
\begin{gathered}(\sin \theta-\operatorname{cosec} \theta)^2+(\cos \theta+\sec \theta)^2=5 \\ \sin ^2 \theta+\operatorname{cosec}^2 \theta-2+\cos ^2 \theta+\sec ^2 \theta+2=5 \\ 1+\cot ^2 \theta+1+\tan ^2 \theta=4 \Rightarrow \tan ^2 \theta+\frac{1}{\tan ^2 \theta}=2 \\…
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