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Question

Prove that: sin1(45)+2tan1(13)=π2

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Solution

Toprovesin1(45)+2tan1(13)=π2now,L.H.S=sin1(45)+2tan1(13)=sin1(45)+tan12×131(13)2[2tan1x=2x1x2]=sin1(45)+tan1(2/38/9)=sin1(45)+tan1(34)=tan1451(45)2+tan1(34)[sin1x=tan1(x1x2)]=tan1(45)+tan1(45)=tan1(45)+cot1(43)[as,tan1(1x)=cot1x]=π2[tanx+cot1x=π2,forallxR]=R.H.SHence,L.H.S=R.H.Sproved

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