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Questions  

The number of real solutions of tan1x(x+1)+sin1x2+x+1=π2 is

a
0
b
1
c
2
d
infinite

detailed solution

Correct option is C

tan−1⁡x(x+1)+sin−1⁡x2+x+1=π2⇒cos−1⁡11+x2+x2+sin−1⁡x2+x+1=π2⇒cos−1⁡11+x2+x2=π2−sin−1⁡x2+x+1=cos−1⁡x2+x+1⇒11+x2+x2=x2+x+1⇒x2+x+1x2+x2+1=1⇒x2+x3+x2+x2+x2+x=0⇒x2+x=0⇒x=−1,0

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