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Question

12tan1x=cos1{1+1+x221+x2}12.

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Solution

12tan1x=cos1{1+1+x221+x2}12

R.H.S Let x=tanθθ=tan1x=cos1{1+1+x221+x2}12=cos1{1+secθ2secθ}12=cos1{1+cosθ2}12=cos1⎪ ⎪ ⎪⎪ ⎪ ⎪2cos2θ22⎪ ⎪ ⎪⎪ ⎪ ⎪12=cos1cosθ2

So, =tan1x2=L.H.S

Proved


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