Statement I : The equation has a solution for all
Statement II : For any ,
Both statements I and II are true.
Both statements I and II are false.
Statement I is true and statement II is false.
Statement I is false and statement II is true.
As we learnt in
Important Results of Inverse Trigonometric Functions -
- wherein
When
Statement 1: cubing both sides
The statement along with (1) becomes
Solution for (2) is
Now (3) is defined only if
However, this is an insufficient condition as sin-1 x is between which will impose additional constraints.
Not true
Statement 2: (true)
Now, attains maxima at and minima at
Hence,
Hence,
Option 1)
Both statements I and II are true.
This option is incorrect.
Option 2)
Both statements I and II are false.
This option is incorrect.
Option 3)
Statement I is true and statement II is false.
This option is incorrect.
Option 4)
Statement I is false and statement II is true.
This option is correct.
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