The number of solution of the equation cos−1(1+x22x)−cos−1x=π2+sin−1x is given by
A
0
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B
1
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C
2
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D
3
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Solution
The correct option is A1 cos−1(1+x22x)=π2+sin−1(x)+cos−1(x) cos−1(1+x22x)=π2+π2 cos−1(1+x22x)=π Taking cos on both the sides, we get 1+x22x=−1 1+x2=−2x 1+2x+x2=0 (1+x)2=0 x=−1 Hence there is only one solution, to the above equation.