If `x=sectheta-costheta` and `y=sec^n theta- cos^n theta` then show that `(x^2+4)((dy)/(dx))^2=n^2(y^2+4)`A. 8B. 16C. 64D. 49

If `x=sectheta-costheta` and `y=sec^n theta- cos^n theta` then show th

1.	If `x=sectheta-costheta` and `y=sec^n theta- cos^n theta` then show that `(x^2+4)((dy)/(dx))^2=n^2(y^2+4)`A. 8B. 16C. 64D. 49
Answer» Correct Answer - C `(dy)/(dx)=(((dy)/(d theta)))/(((dx)/(d theta)))=(8sec^(8) theta tan theta+8cos^(7) thetasin theta)/(sec thetatan theta+sin theta)` `=(8 tan theta(sec^(8)theta+cos^(8)theta)^(2))/(tan theta (sec theta+ cos theta))` `therefore" "((dy)/(dx))^(2)=(64(sec^(8)theta+cos^(8)theta)^(2))/((sec theta+cos theta)^(2))` `=(64[(sec^(8)theta-cos^(8)theta)^(2)+4])/([(sec theta-cos theta)^(2)+4])` `=(64(y^(2)+4))/((x^(2)+4))` `therefore" "((x^(2)+4)/(y^(2)+4))((dy)/(dx))^(2)=64`

The derivative of `cos(2tan^(-1)sqrt((1-x)/(1+x)))-2cos^(-1)sqrt((1-x)/(2))` w.r.t. x isA. `1-(1)/(sqrt(1-x^(2)))`B. `1-(1)/(sqrt(1+x^(2)))`C. `2-(1)/(sqrt(1-x^(2)))`D. `2-(1)/(sqrt(1+x^(2)))`
`(d)/(dx)[cos^(-1)(xsqrtx-sqrt((1-x)(1-x^(2))))]=`A. `(1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))`B. `(-1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))`C. `(1)/(sqrt(1-x^(2)))+(1)/(2sqrt(x-x^(2)))`D. `(1)/(sqrt(1-x^(2)))`
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if `x=(1+t)/t^3 ,y=3/(2t^2)+2/t` satisfies `f(x)*{(dy)/(dx)}^3=1+(dy)/(dx)` then `f(x)` is:A. `x`B. `(x^(2))/(1+X^(2))`C. `x+x+(1)/(x)`D. `x-(1)/(x)`
If `x=sectheta-costheta` and `y=sec^n theta- cos^n theta` then show that `(x^2+4)((dy)/(dx))^2=n^2(y^2+4)`A. 8B. 16C. 64D. 49
A curve parametrically given by `x=t+t^(3)" and "y=t^(2)," where "t in R." For what vlaue(s) of t is "(dy)/(dx)=(1)/(2)`?A. `(1)/(3)`B. 2C. 3D. 1
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