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If sin y = 2sin x show that (dy/dx) squared = 1 +3sec^2 y

luddite

got upto (dy/dx)^2 = (4-4sin^2(x))/cos^y

What identity do i use to change the sin^2 x (sin squared x) to a y

Reply 1

Kevin De Bruyne

Original post by luddite

got upto (dy/dx)^2 = (4-4sin^2(x))/cos^y

What identity do i use to change the sin^2 x (sin squared x) to a y

it appears that you've already given the identity necessary :smile:

Reply 2

Slowbro93

Original post by luddite

got upto (dy/dx)^2 = (4-4sin^2(x))/cos^y

What identity do i use to change the sin^2 x (sin squared x) to a y

Use the information that they've given you in the question to convert from sinx to siny

Then what identies can do you use next?

Reply 3

16Characters....

From the original question sin y = 2sinx. Square both sides.

Reply 4

luddite

yes. thanks:

so far got up to (dy/dx)^2 = (4 - sin^2 y)/cos^2y

dy/dx squared = (4 - sin squared. y) over (cos squared y)

how do i rearrange the sin squared y bit ...which formula do i use

(edited 8 years ago)

Reply 5

luddite

got upto: (dy/dx)^2 = (3 + cos^2y)/(cos^2y) ...what do i do next?

Reply 6

16Characters....

EDIT: Never mind.

You are pretty much there now. Split that fraction up into two.

(edited 8 years ago)

Reply 7

Slowbro93

Original post by luddite

yes. thanks:

so far got up to (dy/dx)^2 = (4 - sin^2 y)/cos^2y

dy/dx squared = (4 - sin squared. y) over (cos squared y)

how do i rearrange the sin squared y bit ...which formula do i use