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If x and y are connected parametrically by the equations, without eliminating the parameter, find dy/dx. x = sin t, y = cos 2t - Mathematics

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प्रश्न

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = sin t, y = cos 2t

योग
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उत्तर

Given, x = sin t and y = cos 2t

Differentiating both sides with respect to t,

`dx/dt = d/dt (sin t)`

= cos t

And `dy/dt = d/dt (cos 2t)`

= `-sin 2t d/dt (2t)`

= −2 sin 2t

`dy/dx = (dy/dt)/(dx/dt)`

= `(-2 sin 2t)/(cos t)`

sin (2t) = 2 sin t cos t

`dy/dx = (-2(2 sin t cos t))/(cos t)`

`dy/dx = (-4 sin t cos t)/(cos t)`

`dy/dx` = −4 sin t

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Continuity and Differentiability - Exercise 5.6 [पृष्ठ १८१]

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एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 5 Continuity and Differentiability
Exercise 5.6 | Q 3 | पृष्ठ १८१

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