Question

Evaluate cos(sin^-1(2x))

Answer 1

evaluate??

Answer 2

by pythagoras you get
\[\sqrt{1-(2x)^2}\] or
\[\sqrt{1-4x^2}\] so
\[\cos(\sin^{-1}(2x))=\sqrt{1-4x^2}\]

Answer 3

I don't understand the way it was worked out.

Answer 4

Find cos( sin^-1(2x) )
Assume sin^-1(2x) = t. We need to find cos(t).

Since sin^-1(2x) = t, it implies sin(t) = 2x

Now refer to the diagram that satellite drew above where the bottom left angle is t.
The dimensions are so chosen in the triangle to make sin(t) = 2x
sin(t) = opposite / hypotenuse = 2x / 1 = 2x

Now we can easily find cosine of the angle t which is adjacent / hypotenuse.
Find the adjacent using Pythagoras Theorem. Hypotenuse = 1. Plug the values and find cos(t).