Question

sin(3sin⁻¹1/3)=.........,Select Proper option from the given options.
(a) 23/27
(b) 1/3
(c) 27/23
(d) 2√3/9

Answer 1

we have to find the value of sin{3sin^-1(1/3)}

Let sin^-1(1/3) = A
sinA = 1/3 ......................(1)

now, sin{3sin^-1(1/3)}= sin(3A)

we know, sin3x = 3sinx - 4sin³x

now, sin3A = 3sinA - 4sin³A

from equations (1),

sin3A = 3 × 1/3 - 4 × (1/3)³

= 1 - 4/27

= 23/27

so, sin{3sin^-1(1/3)}= sin(3A) = 23/27

hence, option (a) is correct.

Answer 2

HELLO DEAR,



GIVEN:-
sin{3sin-¹(1/3)}

Let sin^-1(1/3) = A so, sinA = 1/3

now,

sin{3sin-¹(1/3)} = sin(3A)

WE KNOW:-
sin3x = 3sinx - 4sin³x

therefore,
sin3A = 3sinA - 4sin³A

[as sinA = 1/3]

sin3A = 3 * 1/3 - 4*(1/3)³

= 1 - 4/27 = (27 - 4)/27

= 23/27

so, sin{3sin^-1(1/3)} = sin(3A) = 23/27

hence, option (a) is correct.


I HOPE ITS HELP YOU DEAR,
THANKS