Question

If 4sin⁻¹x+cos⁻¹x=π thenx=.......,Select Proper option from the given options.
(a) - 1/4
(b) 1/4
(c) - 1/2
(d) 1/2

Answer 1

4sin^-1x + cos^-1x = π

4sin^-1x + cos^-1x + 3cos^-1x = π + 3cos^-1x

4sin^-1x + 4cos^-1x = π + 3cos^-1x

4(sin^-1x + cos^-1x) = π + 3cos^-1x

we know, sin^-1x + cos^-1x = π/2 for all |x| ≤ 1

so, 4 × π/2 = π + 3cos^-1x

2π - π = 3cos^-1x

3cos^-1x = π

cos^-1x = π/3

x = cosπ/3 = 1/2


hence, option (d) is correct.

Answer 2

HELLO DEAR,


WE KNOW:-
sin-¹x + cos-¹x = π/2
cos-¹x = (π/2 - Sin-¹x)


NOW,

4sin-¹x + (π/2 - sin-¹x) = π

4sin-¹x - Sin-¹x + π/2 = π

3sin-¹x = π - π/2

3sin-¹x = π/2

sin-¹x = π/6

x = sinπ/6

x = 1/2


hence, option (d) is correct,


I HOPE ITS HELP YOU DEAR,
THANKS