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JEE Mains · Maths · STD 11 - Trigonometrical equations
If \(sin^4\,\,\alpha + 4\,cos^4\,\,\beta + 2 = 4\sqrt 2\,\,sin\,\alpha \,cos\,\beta ;\) \(\alpha \,,\,\beta \, \in \,[0,\pi ],\) then \(cos( \alpha + \beta)\) is equal to
- A \(0\)
- B \(-1\)
- C \(\sqrt 2\)
- D \(-\sqrt 2\)
Answer & Solution
Correct Answer
(D) \(-\sqrt 2\)
Step-by-step Solution
Detailed explanation
\(\mathrm{AM} \geq \mathrm{GM}\) \(\frac{\sin ^{4} \alpha+4 \cos ^{4} \beta+1+1}{4} \geq\left(\sin ^{4} \alpha \cdot 4 \cos ^{4} \beta .1 .1\right)^{\frac{1}{4}}\) \(\sin ^{4} \alpha+4 \cos ^{2} \beta+\) \(2 \geq 4 \sqrt{2} \sin \alpha \cos \beta\) given that…
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