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Which of the following is not a rational number.A. `sin(tan^(-1)3+tan^(-1)((1)/(3)))`B. `cos((pi)/(2)-sin^(-1)((3)/(4)))`C. `log_(2)(sin((1)/(4)sin^(-1)((sqrt(63))/(8)))`D. `tan((1)/(2)cos^(-1)((sqrt(5))/(3))` |
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Answer» Correct Answer - A::B::C (A). `sin(tan^(-1)3+tan^(-1)((1)/(3)))=sin((pi)/(2))=1` (B). `cos((pi)/(2)-sin^(-1)((3)/(4)))=cos(cos^(-1)((3)/(4)))=(3)/(4)` (C). `sin((1)/(4)sin^(-1)((sqrt(63))/(8)))` let `sin^(-1)((sqrt(63))/(8))=theta` `impliessintheta=(sqrt(63))/(8)impliescostheta=(1)/(8)` we have `cos((theta)/(2))=sqrt((1+costheta)/(2))=(3)/(4)` `impliessin((theta)/(4))=sqrt((1-cos((theta)/(2)))/(2))=(1)/(sqrt(2))` now `log_(2)sin((1)/(4)sin^(-1)((sqrt(63))/(8)))=log_(2)(1)/(2sqrt(2))=-(3)/(2)` (D). `cos^(-1)((sqrt(5))/(3))=thetaimpliescostheta=(sqrt(5))/(3)` `becausetan((theta)/(2))=(3-sqrt(5))/(2)` which is irrational |
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