The sum of all values of ∈ (0 , 2 ) satisfying sin^22 + cos^42 = 34 is:

Question

Accepted Answer

Correct answer: C. (c) JEE Main 2019 sin^22 + cos^42 = 34 ⇒1- cos^22 + cos^42 = 34 ⇒ cos^22 (1- cos^22 )= 14 … (i) ∵G .M . A .M . ∴ ( cos^22 )(1- cos^22 ) ( ( cos^22 )(1- cos^22 )2 )= 14 … (ii) So, from equation (i) and (ii), we get G.M. = A.M. It is possible only if, ⇒ cos^22 = 12 ⇒ cos2 = 1 2 ⇒ = 8 , 3 8 ∴Sum = 8+ 3 8= 2

$The sum of all values of θ \in (0, \frac{π}{2}) satisfying sin^{2} 2 θ + cos^{4} 2 θ = \frac{3}{4} is:$

Solution

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