given that siny= 2sinx, show that (dy/dx)^2 = 1 + 3sec^2y
by differentiating this equation with respect to x show that
d^2y/dx^2 = 3sec^2ytany
and hence that coty (d^2y/dx^2) - (dy/dx)^2 + 1 = 0
i havent gotten past the first problem:
differentiating siny=2sinx i get dy/dx= 2cosx/cosy
squaring this i get (dy/dx)^2 = 4cos^2/cos^2y; from here i use the first given statement and double angle identities to get a variety of results such as (4 - siny) x sec^2y but never 1+3sec^2y
can someone please show me exactly how to get to this result?