Is tanh−1(sin⁡2(x+dπ4))=1πln⁡(cot2x)? As you see the above graph that arctan⁡h(sin⁡2(x+π4)) is similar to 1πln⁡(cot2x) Does...

Octavio Miller

Octavio Miller

Answered

2022-01-23

Is tanh1(sin2(x+dπ4))=1πln(cot2x)?
As you see the above graph that arctanh(sin2(x+π4)) is similar to 1πln(cot2x)
Does this mean that by some minor alterations in the functions, they would be equal?
Why are both of functions so similar?

Answer & Explanation

Aaron Hughes

Aaron Hughes

Expert

2022-01-24Added 13 answers

We have
artanh(sin2(x+π4))=artanh(cos2x)=12ln(1+cos2x1cos2x)
=12ln(1+cos2xsin2x1cos2x+sin2x)
=12ln(2cos2x2sin2x)
=12ln(cot2x)

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