Verified Solution • 2025–26 Session moderate

QJEEM07Maeaf3: JEE Main 2007 Mathematics - Class 12 JEEM07Maeaf3 Solution: If sin -1 + cosec -1 = , then the value of x is :

If sin-1 (x5)\left( {{x \over 5}} \right) + cosec-1 (54)\left( {{5 \over 4}} \right) = π2{\pi \over 2} , then the value of x is :

Multiple Choice Options

  • A 4
  • B 5
  • C 1
  • D 3

Step-by-Step Verified Solution

Given sin-1 (x5)\left( {{x \over 5}} \right) + cosec-1 (54)\left( {{5 \over 4}} \right) = π2{\pi \over 2}

⇒\Rightarrow sin-1 (x5)\left( {{x \over 5}} \right) + sin-1 (45)\left( {{4 \over 5}} \right) = π2{\pi \over 2}

⇒\Rightarrow sin-1 (x5)\left( {{x \over 5}} \right) = π2{\pi \over 2} - sin-1 (45)\left( {{4 \over 5}} \right)

⇒\Rightarrow sin-1 (x5)\left( {{x \over 5}} \right) = cos-1 (45)\left( {{4 \over 5}} \right)

⇒\Rightarrow x5{x \over 5} = sin(cos-1 45{{4 \over 5}} )

⇒\Rightarrow x5{x \over 5} = sin(sin-1 35{{3 \over 5}} )

⇒\Rightarrow x5{x \over 5} = 35{3 \over 5}

⇒\Rightarrow x = 3

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