Tanx =-ln integral of absolute value cosx +C, this formula is required to be memorized in higher mathematics.

anx = sinx/cosx∫ 1/x dx = Ln | x |+C？

So: ∫ tan xdx = ∫ sinx/cosdx = ∫-1/cos d cosx =-ln | cosx |+C.

Similarly, there are also

According to: cotx = cosx/sinx ∫1/xdx = ln | x |+c?

So: ∫ cotxdx = ∫ cosx/sinxdx = ∫1/sinxdsinx =-ln | sinx |+C.

Six basic functions

Sine function? sinθ=y/r

Cosine function? cosθ=x/r

Tangent function? tanθ=y/x

Cotangent function? cotθ=x/y

Secant function? secθ=r/x

Cotangent function? csθ= r/y

Equidistant trigonometric function

Square relation:

sin^2(α)+cos^2(α)= 1

tan^2(α)+ 1=sec^2(α)

cot^2(α)+ 1=csc^2(α)