JEE Main202524 Jan 2025Morning ShiftMathematicsInverse Trigonometric FunctionsActual

If for some , ; , + -8 and ^2 ( ⁻¹ )+ cosec ^2 ( ⁻¹ )-36 , then ^2+ is_______.

Correct answer

Step-by-step solution

aligned & Let ⁻¹ =A A= & ⁻¹ =B B= & ^2 A+ cosec ^2 B=36 & 1+ ^2 A+1+ ^2 B=36 & ^2+ ^2=34 aligned Also + =8 (Given) aligned & ( + )^2=34+2 =64 & =15 aligned , are roots of equation aligned & x^2-8 x+15=0 & (x-3)(x-5)=0 & x=3,5 & =3, =5 ( < ) & ^2+ =9+5=14 aligned

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