- #1

Byeonggon Lee

- 14

- 2

I only memorized these trigonometric differential identities :

`sin(x) = cos(x)

`cos(x) = -sin(x)

because I can convert tan(x) to sin(x) / cos(x) and

sec(x) to 1 / cos(x) .. etcAnd there is no need to memorize some integral identities such as :

∫ sin(x) dx = -cos(x) + C

∫ cos(x) dx = sin(x) + C

because I memorized

`sin(x) = cos(x)

`cos(x) = -sin(x)But these identities seem inevitable to memorize:

∫ sec^2(x) dx = tan(x) + C

∫ cosec^2(x) dx = -cot(x) + C

∫ sec(x)tan(x) dx = sec(x) + C

∫ cosec(x)cot(x) dx = -cosec(x) + C

For example

∫ sec^2(x) dx = tan(x) + C

First I tried to convert sec^2(x) to 1 / cos^2(x)

∫ sec^2(x) dx = ∫ (1 / cos^2(x)) dx

And that's where I'm stuck.

It looks impossible to proceed anymore without memorizing a trigonometric differential identity

`tan(x) = sec^2(x)

`sin(x) = cos(x)

`cos(x) = -sin(x)

because I can convert tan(x) to sin(x) / cos(x) and

sec(x) to 1 / cos(x) .. etcAnd there is no need to memorize some integral identities such as :

∫ sin(x) dx = -cos(x) + C

∫ cos(x) dx = sin(x) + C

because I memorized

`sin(x) = cos(x)

`cos(x) = -sin(x)But these identities seem inevitable to memorize:

∫ sec^2(x) dx = tan(x) + C

∫ cosec^2(x) dx = -cot(x) + C

∫ sec(x)tan(x) dx = sec(x) + C

∫ cosec(x)cot(x) dx = -cosec(x) + C

For example

∫ sec^2(x) dx = tan(x) + C

First I tried to convert sec^2(x) to 1 / cos^2(x)

∫ sec^2(x) dx = ∫ (1 / cos^2(x)) dx

And that's where I'm stuck.

It looks impossible to proceed anymore without memorizing a trigonometric differential identity

`tan(x) = sec^2(x)

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