Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202619 April 2026Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

The value of ( 5 ) is ...

Options

  1. A-1 + 5 4
  2. B-1 + 5 2
  3. C1 + 5 4
  4. D1 - 5 4

Correct answer

C. 1 + 5 4

Step-by-step solution

Let x = 5 . 5x = 2x = - 3x Taking sine on both sides: (2x) = ( - 3x) (2x) = (3x) 2 x x = 3 x - 4 ^3 x Since x 0 , dividing by x gives: 2 x = 3 - 4 ^2 x 2 x = 3 - 4(1 - ^2 x) 4 ^2 x - 2 x - 1 = 0 Solving the quadratic equation for x : x = 2 4 - 4(4)(-1) 2(4) = 2 20 8 = 1 5 4 Since x = 5 lies in the first quadrant, x > 0 . Therefore, ( 5 ) = 1 + 5 4 Answer: 1 + 5 4

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 MHT CET PYQs