Question

15. Number of solutions of the equation (sin-'x)³+(cos-'x)³ = 2(pie)³ is
a) O
b) 1
c)2
d) infinite​

Answer 1

Answer:

Say f(x)=(sin

−1

x)

3

+(cos

−1

x)

3

f

′

(x)=0 at x=

4

π

f

′′

(x)≥0 at x=

4

π

so f(x)=

32

π

3

This is least value.

∴f(x)≥aπ

3

has a solution.

∴

32

1

≥ a

Statement I is incorrect.

Now

2

−π

≤sin

−1

x≤

2

π

0≤(sin

−1

x−

4

π

)

2

≤

16

9π

2

Min at x=

4

π

and max at x=

2

π

. So, Statement I is incorrect and II is correct.

I want to help u but im not sure is it correct