JEE Mains · Maths · STD 11 - Trigonometrical equations
If \(\mathrm{n}\) is the number of solutions of the equation \(2 \cos x\left(4 \sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac{\pi}{4}-x\right)-1\right)=1, x \in[0, \pi]\) and \(S\) is the sum of all these solutions, then the ordered pair \((\mathrm{n}, \mathrm{S})\) is :
- A \((3,13 \pi / 3)\)
- B \((2,2 \pi / 3)\)
- C \((2,8 \pi / 9)\)
- D \((3,5 \pi / 3)\)
Answer & Solution
Correct Answer
(A) \((3,13 \pi / 3)\)
Step-by-step Solution
Detailed explanation
\(2 \cos x\left(4 \sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac{\pi}{4}-x\right)-1\right)=1\) \(2 \cos x\left(4\left(\sin ^{2} \frac{\pi}{4}-\sin ^{2} x\right)-1\right)=1\) \(2 \cos x\left(4\left(\frac{1}{2}-\sin ^{2} x\right)-1\right)=1\)…
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