Question

sin{π/3 - sin⁻¹(- 1/2)} is........,Select Proper option from the given options.
(a) 0
(b) 1/2
(c) √3/2
(d) 1

Answer 1

it is given that $sin[\frac{\pi}{3}-sin^{-1}(-1/2)]$

or, $sin[\frac{\pi}{3}+sin^{-1}(1/2)]$

Let sin^-1(1/2) = A
sinA = 1/2 ........(1)
cosA = √3/2 .......(2)

now,use formula sin(C + D) = sinC.cosD + cosC.sinD

sin(π/3 + A) = sinπ/3.cosA + sinA.cosπ/3
= √3/2 × √3/2 + 1/2 × 1/2 [ from eqs (1) and (2)]
= (√3/2)² + (1/2)²
= 3/4 + 1/4
= 4/4
= 1

hence, option (d) is correct.

Answer 2

HELLO DEAR,


GIVEN:-
sin{π/3 - sin-¹ (-1/2)}

sin{π/3 + sin-¹ (1/2)}

[ sin-¹ (1/2) = π/6]

therefore, sin{π/3 + π/6}

= sin(π/2)

= 1


hence, option (d) is correct



I HOPE ITS HELP YOU DEAR,
THANKS