Question

x=a(cos t + log tan t/2) y = a sin t find dy/dx

Answer 1

dy/dx = Tant     , x=a(cos t + log tan t/2)  , y = a sin t

Step-by-step explanation:

x=a(cos t + log tan t/2)

y = a sin t

y = a sin t

dy/dt  = aCost

x=a(cos t + log tan t/2)

dx/dt  = a( -Sint  +  (1/Tan(t/2))( Sec²(t/2))  (1/2)

dx/dt  = a( -Sint  +  (1/2Cos²(t/2)Tan(t/2))

dx/dt  = a( -Sint  +  (1/2Cos(t/2)Sin(t/2))

dx/dt  = a( -Sint  +  1/Sint)

dx/dt  = a( -Sin²t  +  1/)/Sint

dx/dt  = a(Cos²t)/Sint

(dy/dt )/(dx/dt) = aCost /a(Cos²t)/Sint

=> dy/dx = Sint/Cost

=> dy/dx = Tant

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