Math

posted by .

can you prove this equation for me?

sin2x X sec2x = 2sinx

• Math -

by "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.

Similar Questions

1. trigonometry

if sin2x=3sin2y, prove that: 2tan(x-y)=tan(x+y) ( here, in sin2x, 2x is an angle., like there's a formula:sin2x=2sinxcosx and sin2y=2sinycosy; ....)

3. math

prove: 2sinx+sin2x = 2sin^3(x)/1-cosx
4. Trigonometry

Verify the identity. sin2x/cosx + sinx = 2sinx Solve for all values of x: 6cos2x-7cosx-3=0 If f(x)=cos1/2x-sin2x find the value of f(pi)
5. Precalculus

Determine the solutions to the equation 2sinx − cos2x = sin2x for 0 ≤ x ≤ 2π . How do I start this question?
6. Math

Prove 1+sec2x / tan2x = cotx
7. Trigonometry

Let's solve this fun trigonometric fun math problem! 1.) SEC²X-1/SIN²X
8. Trigonometry

Verify the identities algebraically. 1.) TAN^5 X= TAN³X SEC²X-TAN³X 2.) COS³X SIN²X= (SIN²X-SIN^4X)COS X