WBJEE · Maths · Determinants
The number of distinct real roots of \(\left|\begin{array}{lll}\sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x\end{array}\right|=0\) in the interval \(-\frac{\pi}{4} \leq x \leq \frac{\pi}{4}\) is
- A 0
- B 2
- C 1
- D >2
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
Given, \(\left|\begin{array}{ccc}\sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x\end{array}\right|=0\) \(\sin x\left(\sin ^{2} x-\cos ^{2} x\right)-\cos x\left(\sin x \cos x-\cos ^{2} x \right ) + \cos x \left(\cos ^{2} x-\sin x \cos x\right)=0\)…
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