#### Statement I :     The   equation  has a solution for all Statement II :   For any , Option 1)  Both statements I and II are true.   Option 2)  Both statements I and II are false. Option 3)  Statement I is true and statement II is false.   Option 4)   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.