Question

Simplify by referring to the appropriate triangle or trigonometric identity. (Use symbolic notation and fractions where needed.) cot[sin−1(12)]=cot⁡[sin−1⁡(12)]= help (fractions)

Answer 1

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