Question

What is this TRIG identity called. see attachment.

Answer 1

@dan815

Answer 2

@LynFran

Answer 3

@jim_thompson5910

Answer 4

I'm not sure if there is a specific name for this identity

Answer 5

how would I explain it though

Answer 6

I guess you could say "composition of a trig function and another inverse" ? I'm not sure

Answer 7

oh you want to know how they got that identity?

Answer 8

yeah

Answer 9

here let me give you an example

Answer 10

tan(arccos(x))

let theta = arccos(x)

so cos(theta) = x = x/1

agreed?

Answer 11

\[\tan(\cos^-1(1/2)\]

Answer 12

yes agreed

Answer 13

so we can create this right triangle

Answer 14

cos(theta) = x/1

cosine deals with adjacent over hypotenuse

Answer 15

so we can add these labels

Answer 16

what is the missing side equal to (in terms of x) ?

Answer 17

1^2-x^2

Answer 18

it will be the square root of that