JEE Mains · Maths · STD 11 - Trigonometrical equations
Let \(S\) be the sum of all solutions (in radians) of the equation \(\sin ^{4} \theta+\cos ^{4} \theta-\sin \theta \cos \theta=0\) in \([0,4 \pi]\) Then \(\frac{8 \mathrm{~S}}{\pi}\) is equal to ...... .
- A \(87\)
- B \(78\)
- C \(56\)
- D \(65\)
Answer & Solution
Correct Answer
(C) \(56\)
Step-by-step Solution
Detailed explanation
Given equation \(\sin ^{4} \theta+\cos ^{4} \theta-\sin \theta \cos \theta=0\) \(\Rightarrow 1-\sin ^{2} \theta \cos ^{2} \theta-\sin \theta \cos \theta=0\) \(\Rightarrow 2-(\sin 2 \theta)^{2}-\sin 2 \theta=0\) \(\Rightarrow(\sin 2 \theta)^{2}+(\sin 2 \theta)-2=0\)…
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