TS EAMCET · Maths · Trigonometric Ratios & Identities
If \(\sin \theta+\cos \theta=p\) and \(\sin ^3 \theta+\cos ^3 \theta=q\), then \(p\left(p^2-3\right)\) is equal to
- A \(q\)
- B \(2 q\)
- C \(-q\)
- D \(-2 q\)
Answer & Solution
Correct Answer
(D) \(-2 q\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Given, } \quad \sin \theta+\cos \theta=p \\ & \text { and } \quad \sin ^3 \theta+\cos ^3 \theta=q \\ & \Rightarrow \quad(\sin \theta+\cos \theta) \\ & \quad\left(\sin ^2 \theta-\sin \theta \cdot \cos \theta+\cos ^2 \theta\right)=q\end{aligned}\)…
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