Friday

August 26, 2016
Posted by **Alex** on Friday, March 25, 2011 at 5:20pm.

sin2x X sec2x = 2sinx

- Math -
**Reiny**, Friday, March 25, 2011 at 5:38pmby "proving" an equation , we usually mean to show that it is an identity.

but it is NOT an identity.

(I usually just try it with an arbitrary angle)

sin2x/cos2s = 2sinx

tan 2x = 2sinx

let x= 30°

LS = tan 60 = √3

RS = 2sin30 = 2(1/2) = 1

LS ≠ RS

So it is not an identity, (all we need is one exception)

If you are solving for x, then

2sinx cosx (1/cos2x) = 2sinx

2sinxcosx(1/(2cos^2x - 1) = 2sinx

2sinxcosx = 2sinx(2cos2x - 1)

2sinxcosx - 2sinx(2cos^2x - 1) = 0

2sinx [ cosx - 2cos^2x + 1] = 0

2sinx = 0 or 2cos^2x - cosx - 1) = 0

sinx = 0

x = 0, 180°, 360°

2cos^2x - cosx - 1) = 0

(2cosx + 1)(cosx - 1) = 0

cosx = -1/2 or cosx = 1

cosx = -1/2

x = 120°, 240°

cosx = -1

x = 270°

x = 0, 180, 360, 120, 240, 270 °

I gave the angles in degrees, and in the domain between 0 and 360

I assume you know how to change them to radians if necessary.