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in all of these, you can replace everything with sin and cos, then multiply everything until it becomes definitionally true, or pythagorean identity

well, they're all true

establish the identity means show the fact that it's true

use some steps to prove the equation is correct

for any angle

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i told you
replace everything with sin and cos
multiply both sides by things to remove the fractions
pythag identity

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recall the definitions of cot, tan, sec, and plug those in

x is an angle just like theta

different letter yeah

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yeah

though in the last step you don't need to multiply both sides by sin x

it might be easier just to cancel out the fraction with the sin x thats already on the right hand side

but, your method works too

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you were close on the line

sin^2theta/costheta + costheta = 1/costheta

try multiplying both sides by the denominator of the fractions

also sorry for slow response

remember, when you multiply one side of the equation, you multiply every added term by that thing

so that means you should also multiply the cos

by cos

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again, multiply everything so that the fractions go away

ah yes

so

1/cosx * 1/sinx * cosx

you don't multiply everything by cosx

because in this case, they are being multiplied

multiplicatino doesn't distibute over addition

what i mean is
(a + b)c = ac + bc
(a x b)c is not ac x bc

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so, this should only become 1/sin(x)

yes

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e

hmm
multiplication is like finding the area of a rectangle
multiplying 3 things is like volume of a solid

you can split a rectangle up into 2 rectangles (this is why it distributes over addition), you cant turn finding volume into finding 2 areas and multiplying them together
volume of a prism is always just base times height