Prove that :

tan-1(1/4) + tan-1(2/9) = 1/2 Cos-1 (3/5)

To prove:

LHS:

This can be written as:

 

= RHS

Hence proved.

  • 68

L.H.S = tan-1(1/4)+tan-1(2/9) = tan-1(1/4+2/9)/(1-1/4*2/9) = tan-1(1/2) = 1/2*2tan-1(1/2)

  = 1/2cos-1(1-1/4)/(1+1/4) = 1/2cos-1(3/5)

  • -12
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