JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
Let the set of all \(a \in R\) such that the equation \(\cos 2 x+a \sin x=2 a-7\) has a solution be \([p, q]\) and \(\mathrm{r}=\tan 9^{\circ}-\tan 27^{\circ}-\frac{1}{\cot 63^{\circ}}+\tan 81^{\circ}\), then \(pqr\) is equal to ...........
- A \(62\)
- B \(55\)
- C \(48\)
- D \(45\)
Answer & Solution
Correct Answer
(C) \(48\)
Step-by-step Solution
Detailed explanation
\(\cos 2 x+a \cdot \sin x=2 a-7 \) \( a(\sin x-2)=2(\sin x-2)(\sin x+2) \) \( \sin x=2, \quad a=2(\sin x+2) \) \( \Rightarrow a \in[2,6] \) \( p=2 \quad q=6\) \( r=\tan 9^{\circ}+\cot 9^{\circ}-\tan 27-\cot 27 \)…
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