InterviewSolution
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InterviewSolution
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If `tan^-1x, tan^-1y` and `tan^-1z` are in A.P. then find the algebraic relation between x,y and z. If `x,y,z` are also in A.P. then show that `x=y=z` and `y!=0`A. `x=y=zory!=1`B. `x=1//z`C. x=y=z, but their common value is not necessarily zeroD. x=y=z=0 |
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Answer» Correct Answer - C `:." "y^(2)=xz` . . .(i) Also, `tan^(-1)x,tan^(-1)y,tan^(-1)z` are in A.P. `:." "2tan^(-1)y,tan^(-1)x,tan^(-1)z` `rArr" "tan^(-1)((2y)/(a-y^(2)))=tan^(-1)((x+z)/(1-xz))` `rArr" "(2y)/(1-y^(2))=(x+z)/(1-xz)` `rArr" "(2y)/(1-xz)=(x+z)/(1-xz)" [Using (i)]"` `rArr" "` x,y,z are in A.P. . . . (ii) From (i) and (ii), we get x=y=z |
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