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Question

The sum of solutions of equation 2sin1x2+x+1+cos1x2+x=3π2 is λ then λ equals 


Solution

0(x2+x+1)1 and 0(x2+x)1

which holds together for x=1, 0

At x=1, L.H.S. =2sin1+cos10

=π+π2=3π2

At x=0, L.H.S. =π+π2=3π2

Sum of the solutions =1+0=1=λ
λ=1

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