- #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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