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  • Prove that : tan (pi/4+1/2 cos^-1 a/b)+tan(pi/4-1/2 cos^-1 a/b)=2b/a

Prove that : tan (pi/4+1/2 cos^-1 a/b)+tan(pi/4-1/2 cos^-1 a/b)=2b/a

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Solution:  Let cos^-1(a/b)= heta   Then , cos heta =a/b

              Rightarrow     LHS= an(pi/4+ heta /2)+ an(pi/4- heta /2)

             Rightarrow     LHS=[(1+ an heta /2)/(1- an heta /2)]+[(1- an heta /2)/1+ an heta /2]

                           LHS=2/cos heta =2(b/a)  

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Deependra Verma

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