JEE Mains · Maths · STD 11 - Trigonometrical equations
The number of solutions of \(\sin ^{7} x+\cos ^{7}=1, x \in[0,4 \pi]\) is equal to :
- A \(5\)
- B \(9\)
- C \(11\)
- D \(7\)
Answer & Solution
Correct Answer
(A) \(5\)
Step-by-step Solution
Detailed explanation
\(\sin ^{7} x \leq \sin ^{2} x \leq 1....(1)\) \(\text { and } \cos ^{7} x \leq \cos ^{2} x \leq 1....(2)\) \(\text { also } \sin ^{2} x+\cos ^{2} x=1\) \(\Rightarrow \text { equality must hold for }(1) \,\,(2)\) \(\Rightarrow \sin ^{7} x=\sin ^{2} x \,\, \cos ^{7}=\cos ^{2} x\)…
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