Trigonometric Functions

For , (0, /2), let 3 ( + )=2 ( - ) and a real number k be such that =k . Then, the value of k is equal to

1. 5
2. -2/3
3. -5
4. 2/3

Answer

BONUS

Solution

3( + )=2( - )

=-5 =-5 , i.e. k=-5

But , (0, 2 ) >0 and >0, so =-5 can never hold

∵ no such , exist, the data are inconsistent ⇒ question dropped

Answer: Bonus (full marks to all who attempted)

Note: The official NTA answer key gives option (3). Our faculty team finds that no option is fully correct, so this question should be dropped (bonus: full marks to everyone who attempted it).