InterviewSolution
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InterviewSolution
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If `0< x< 1`,then `tan^(-1)(sqrt(1-x^2)/(1+x))` is equal toA. `1/2 cos^(-1)x`B. `cso^(-1)sqrt(1+x)/(2)`C. `sin^(-1)sqrt(1-x)/(2)`D. all the above |
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Answer» Let `x = cos theta` Then `0ltxlt1 rarr 0ltcos theta lt1 rarr0lttheta lt(pi)/(2)` Now `tan^(-1)sqrt(1-x^(2))/(1+x)` `tan^(-1)sqrt(1-x^(2)/(1+x)` Thus option (a)is true `cos^(-1)sqrt(1+x)//(2)=cos^(-1)(cos(theta)/(2))=1/2theta=1/2 cos^(-1)x` so option (b) is true `sin^(-1)sqrt(1-x)/(2)=sin^(-1)(sin(theta)/(2))=1/2theta=1/2cos^(-1)x` `sin^(-1)sqrt(1-x)/(2)=sin^(-1)(sin(theta)/(2))=(theat)/(2)=(1)/(2)cosT^(-1)x` so option (c ) is true |
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