COMEDK2025MathematicsTrigonometric Ratios & IdentitiesActual
If = 1 7 and = 1 10 , 0 < , < 2 then 2 is equal to
Options
- A3 4 -
- B3 8 - 2
- C4 -
- D8 -
Correct answer
C. 4 -
Step-by-step solution
Given = 1 7 and = 1 10 . Since = 1 10 , we have = 1 - ^2 = 1 - 1 10 = 9 10 = 3 10 . Therefore, = = 1/ 10 3/ 10 = 1 3 . We calculate 2 using the formula 2 = 2 1 - ^2 . 2 = 2(1/3) 1 - (1/3)^2 = 2/3 1 - 1/9 = 2/3 8/9 = 2 3 9 8 = 3 4 . Now consider ( + 2 ) = + 2 1 - 2 . Substituting the values, ( + 2 ) = 1/7 + 3/4 1 - (1/7)(3/4) = (4+21)/28 (28-3)/28 = 25/28 25/28 = 1 . Since 0 Since = 1/7 and = 1/3 , both and are small positive angles, so + 2 must be 4 . Thus, 2 = 4 - . Answer: 4 -