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The equation $\tan^{2} x + \cot^{2} x = 4 a {cosec}^{2} 2 x$ has $a$ real solution if

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1/2≤a≤1

1/4≤a≤1/2

−1≤a≤1

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detailed solution

Correct option is B

a=sin2⁡x+cos2⁡x2−2sin2⁡xcos2⁡x⇒sin2⁡2x=−2(a−1)⇒1−cos⁡4x=−4(a−1)⇒cos⁡4x−4a−3so−1≤4a−3≤1⇒1/2≤a≤1

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The equation tan2⁡x+cot2⁡x=4acosec2⁡2x has a real solution if

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Ready to Test Your Skills?

free study material

The equation $\tan^{2} x + \cot^{2} x = 4 a {cosec}^{2} 2 x$ has $a$ real solution if