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# implicit function watch

1. Sin (y) = 2Sin(x)
Show that (dy/dx)^2= 1 + 3sec^2(y)

dy/dx . Cos(y) = 2(-Cos(x))

dy/dx = -2Cos(x)/Cos(y)

(dy/dx)^2 = 4Cos^2(x)/Cos^2(y)

Squaring initial equation
Sin^2(y) = 4Sin^2(x) => Sin^2(y) = 4(1-Cos^2(x)) => Sin^2(y) = 4-4Cos^2(x)
Rearranging this we get
4Cos^2(x)=4-Sin^2(y)

So,
(dy/dx)^2 = 4 - Sin^2(y)/Cos^2(y)

(dy/dx)^2 =4Sec^2(y) - tan^2(y)

I dont know how to continue
2. (Original post by Carlos Nim)
So,
(dy/dx)^2 = 4 - Sin^2(y)/Cos^2(y)

(dy/dx)^2 =4Sec^2(y) - tan^2(y)

I dont know how to continue
3. Thank you again. Omg why cant i see these simple things

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