Answer:
The correct question is:
Simplify by referring to the appropriate triangle or trigonometric identity. (Use symbolic notation and fractions where needed.) cot[sin−1(1/2)]
Answer:
cot(sin^(-1)1/2) = 1/√3
Step-by-step explanation:
To simplify cot(sin^(-1)1/2)
Let a = sin^(-1)1/2
Then sin(a) = 1/2
and
cot(sin^(-1)1/2) = cot(a)
Since
sin(a) = 1/2
a = π/6
cot(a) = 1/tan(a) = sin(a)/cos(a)
But cos(a) = cos(π/6) = (√3)/2
So
cot(π/6) = sin(π/6)/cos(π/6)
= (1/2)/((√3)/2)
= (1×2)/((√3)×2)
= 2/2√3
= 1/√3
