How do you solve cot parenthesis inverse of sin 4 over 7 closed parenthesis?

The inverse sin function I write as arcsin x.

Make use of the trignometric relationships:

cos2θ + sin2θ = 1

⇒ cosθ = √(1 - sin2θ)

cotθ = cosθ/sinθ

= √(1 - (sinθ)2)/sinθ

sin(arcsin x) = x

Then:

cot(arcsin(x)) = √(1 - (sin(arcsin(x))2)/sin(arcsin(x))

= √(1 - x2)/x

⇒ cot(arcsin(4/7)) = √(1 - (4/7)2)/(4/7)

= √(49/72 - 16/72) ÷ 4/7

= √(49 - 16) x 1/7 x 7/4

= 1/4 x √33