InterviewSolution
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InterviewSolution
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If ` y=a sin x + b cos x`, then `((dy)/dx)^2+y^2` isA. function of xB. function of yC. function of x and yD. constant |
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Answer» y=a sin x + b cos x Differentiating with respect to x, we get `(dy)/(dx)=a cos x - b sin x` `"Now, "((dy)/(dx))^(2)=(a cos x - b sin x)^(2)` `=a^(2)cos^(2)x+b^(2)sin^(2)x-2ab sin x cos x` `"and "y^(2)=(a sin x + b cos x)^(2)` `a^(2)sin^(2) x +b^(2)cos^(2) x +2ab sin x cos x` `"So, "((dy)/(dx))^(2)+y^(2)=a^(2)(sin^(2)x + cos^(2)x)+b^(2)(sin^(2)x+ cos^(2)x)` `=(a^(2)+b^(2))=` constant |
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