Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202316 May 2023Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If ( - ), and ( + ) are in harmonic progressions, then 2 ^2 =

Options

  1. A^2 2 -1
  2. B1+ ^2 2
  3. C1+ ^2 2
  4. D1- ^2 2

Correct answer

A. ^2 2 -1

Step-by-step solution

Given, ( - ), and ( + ) are in harmonic progression 2 = ( + )+ ( - ) ( - ) ( + ) aligned & = 2 ( - ) ( + ) ( - )+ ( + ) & 2 ( - ) ( + ) 2 aligned aligned & = ^2 ^2 - ^2 ^2 & = ^2 ^2 - (1- ^2 ) ^2 & = ^2 ^2 + ^2 ^2 - ^2 & ^2 = ^2 - ^2 & ^2 = ^2 1- = 4 ^2 2 2 ^2 2 ^2 2 =2 ^2 2 & ^2 =1-2 ^2 2 & Now, ^2 = 1-2 ^2 2 2 ^2 2 = 1 2 ^2 2 -1 & 2 ^2 = ^2 2 -2 & 2 ^2 = ^2 2 -1 . aligned

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 AP EAMCET PYQs