Verified Solution • 2025–26 Session moderate

QJEEM19Made81: JEE Main 2019 Mathematics - Class 11 JEEM19Made81 Solution: The sum of all values of satisfying sin 2 2 + cos 4 2 = is -

The sum of all values of θ\theta ∈\in (0,π2)\left( {0,{\pi \over 2}} \right) satisfying
sin2 2 θ\theta + cos4 2 θ\theta = 34{3 \over 4} is -

Multiple Choice Options

  • A 5π4{{5\pi } \over 4}
  • B π2{\pi \over 2}
  • C π\pi
  • D 3π8{{3\pi } \over 8}

Step-by-Step Verified Solution

sin22 θ\theta + cos42 θ\theta = 34,{3 \over 4}, θ\theta ∈\in (0,π2)\left( {0,{\pi \over 2}} \right)

⇒\Rightarrow   1 −- cos22 θ\theta + cos42 θ\theta = 34{3 \over 4}

⇒\Rightarrow   4cos2 θ\theta −- 4cos22 θ\theta + 1 = 0

⇒\Rightarrow   (2cos22 θ\theta −- 1)2 = 0

⇒\Rightarrow   cos22 θ\theta = 12{1 \over 2} = cos2 π4{{\pi \over 4}}

⇒\Rightarrow   2 θ\theta = n π\pi ±\pm π4{\pi \over 4} , n ∈\in I

⇒\Rightarrow    θ\theta = nπ2±π8{{n\pi } \over 2} \pm {\pi \over 8}

⇒\Rightarrow    θ\theta = π8,π2−π8{\pi \over 8},{\pi \over 2} - {\pi \over 8}

Sum of solutions π2{\pi \over 2}

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