InterviewSolution
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InterviewSolution
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If `y=cot^(-1)sqrt((1-sinx)/(1+sinx)),` find `(dy)/(dx).` |
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Answer» We have `y=cot^(-1)sqrt((1-sinx)/(1+sinx))="cot"^(-1)sqrt(1+cos((pi)/(2)+x)/(1-cos((pi)/(2)+x)))` `="cot"^(-1)sqrt((2cos^(2)((pi)/(4)+(x)/(2)))/(2sin^(2)((pi)/(4)+(x)/(2))))=cot^(-1){cot((pi)/(4)+(x)/(2))}=((pi)/(4)+(x)/(2)).` `therefore(dy)/(dx)=(d)/(dx)((pi)/(4)+(x)/(2))=(d)/(dx)((pi)/(4))+(d)/(dx)((x)/(2))=(0+(1)/(2))=(1)/(2).` |
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