Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2024Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If = 1 2 (x+ 1 x ) then 1 2 (x^2+ 1 x^2 )=

Options

  1. A^2 - ^2
  2. B2 ( ^2 - ^2 )
  3. C^2 - ^2
  4. D1 2 ( ^2 - ^2 )

Correct answer

A. ^2 - ^2

Step-by-step solution

Given = 1 2 (x + 1 x ) , we have x + 1 x = 2 . Squaring both sides: (x + 1 x )^2 = (2 )^2 x^2 + 1 x^2 + 2 = 4 ^2 x^2 + 1 x^2 = 4 ^2 - 2 Now, we need to find 1 2 (x^2 + 1 x^2 ) : 1 2 (x^2 + 1 x^2 ) = 1 2 (4 ^2 - 2) = 2 ^2 - 1 . Using the identity ^2 + ^2 = 1 , we can write 1 = ^2 + ^2 . Substituting this into the expression: 2 ^2 - ( ^2 + ^2 ) = ^2 - ^2 . Answer: ^2 - ^2

Practice Trigonometric Ratios & Identities on Quantrex Academy →

More from Trigonometric Ratios & Identities

If x+ x= 1 2 and 0 < x < , then x= 2025If A and B are acute angles satisfying 3 ^2 A+2 ^2 B=4 and 3 A B = 2 B A , then A+2 B= 2025In a ABC , if ^2 ~B = A and 2 ^2 ~A =3 ^2 ~B , then the triangle is 202512 2 12 3 12 4 12 5 12 6 12 = 2025If ( 4 + )= ^3 ( 4 + ) , then ( + ) ( - )= 2025If A+B+C+D=2 , then A+ B+ C+ D= 2025(4 ^2 20 -1 ) (4 ^2 3 20 -1 ) (4 ^2 5 20 +1 ) (4 ^2 7 20 -1 ) (4 ^2 9 20 -1 )= 2025If A and B are the values such that (A+B) and (A-B) are not odd multiples of 2 and 2 (A+B)=3 (A-B) , then A A= 2025 Full Trigonometric Ratios & Identities list All COMEDK PYQs