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power series for tanhֿ¹x


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 show that tanhֿ¹x = x + (x³/3) +  ...    for lxl<1
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take y =tanhֿ¹x
differentiate once
then expand the result as a power series
integrate to get tanhֿ¹x
answer and  some steps are given below
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notes on hyperbolic function

(trig. formulae) 
some other examples
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find exact value of  tan[22½ °]   or tan (pi / 8 )      -----> (problem on trigonometry )

conditional identity : If A+B+C=π,
prove that: sinA+sinB+sinC = cot(A/2).cot(B/2) [sinA+sinB-sinC] -----> (problem on conditional identity (trigonometry) )



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