MHT CET202619 April 2026Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual
The value of ( 5 ) is ...
Options
- A-1 + 5 4
- B-1 + 5 2
- C1 + 5 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