Question

Sin inverse 1 by 2 + Cos inverse 1 by 2 is equal to

Answer 1

method 1:-

sin^-1(1/2) + cos^-1(1/2)

we know,
cos^-1(x) + sin^-1(x) = π/2

here x = 1/2

hence,
sin^-1(1/2) + cos^-1(1/2) = π/2


method 2 :-

Let sin^-1(1/2) = A
sinA = 1/2
sinA = sin(π/6)
A = π/6

again,
cos^-1(1/2) = B
cosB = 1/2
cosB = cos(π/3)
B = π/3

hence,

sin^-1(1/2) + cos^-1(1/2) = A + B = π/2

Answer 2

Answer:

5Π /12

cos ^-1   1/2 =x

sin^-1     1/2=x

then,

cos x=1/2

sin x/2=1/2

sinx/2=Π/12

cos x =Π/3