Question

X= a ( cos t + t sin t), y= a( sin t - t cos t) find dy/ dx

Answer 1

$\underline{\textbf{\large{Step-by-step explanation:}}}$

x = a ( cos t + t sint)

$\underline{\textbf{differentiate wrt t :}}$

dx / dt = d /dt ( a (cos t + t sin t))

= ( a ( -sint + (t x cos t + sint x 1 )))

= (a ( -sint +t cost + sin t ))

= (a ( t cos t))

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Now,

y = a( sin t - t cos t)

$\underline {\textbf{differentiate wrt t : }}$

dy / dt

= d/dt(a(cost - ( t (-sin t )+(cost) 1)))

= (a(cost + t sint - cos t))

= (a (t sin t))

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We know,

$\underline{\textbf{dy/dx= (dy/dt)/(dx/dt)}}$

therefor ,

dy /dx = (a (t sin t)) / (a ( t cos t))

= sint / cost

= tan t

$\boxed{\underline{\textbf{\large{dy/dx= tan t }}}}$

Answer 2

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