How do you prove $sin x = 1 - 2 {cos}^{2} x$ $sin x = 1 - 2 cos^2x$ ?

Question

How do you prove $sin x = 1 - 2 {cos}^{2} x$ $sin x = 1 - 2 cos^2x$ ?

1 Answer

Related questions

What does it mean to prove a trigonometric identity?
How do you prove $csc θ \times tan θ = sec θ$ $\csc \theta \times \tan \theta = \sec \theta$ ?
How do you prove $(1 - {cos}^{2} x) (1 + {cot}^{2} x) = 1$ $(1-\cos^2 x)(1+\cot^2 x) = 1$ ?
How do you show that $2 sin x cos x = sin 2 x$ $2 \sin x \cos x = \sin 2x$ ? is true for $\frac{5 π}{6}$ $(5pi)/6$ ?
How do you prove that $sec x cot x = csc x$ $sec xcot x = csc x$ ?
How do you prove that $cos 2 x (1 + tan 2 x) = 1$ $cos 2x(1 + tan 2x) = 1$ ?
How do you prove that $\frac{2 sin x}{sec x (cos 4 x - sin 4 x)} = tan 2 x$ $(2sinx)/[secx(cos4x-sin4x)]=tan2x$ ?
How do you verify the identity: $- cot x = \frac{sin 3 x + sin x}{cos 3 x - cos x}$ $-cotx =(sin3x+sinx)/(cos3x-cosx)$ ?
How do you prove that $\frac{tan x + cos x}{1 + sin x} = sec x$ $(tanx+cosx)/(1+sinx)=secx$ ?
How do you prove the identity $\frac{sin x - cos x}{sin x + cos x} = \frac{2 {sin}^{2} x - 1}{1 + 2 sin x cos x}$ $(sinx - cosx)/(sinx + cosx) = (2sin^2x-1)/(1+2sinxcosx)$ ?

Impact of this question

2078 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-16T23:44:49

For $x = \frac{π}{6}$ $x=pi/6$ :
$sin (x) = \frac{1}{2}, cos (x) = \frac{\sqrt{3}}{2}$ $sin(x) = 1/2, cos(x) = sqrt(3)/2$
$1 - 2 \cdot {(\frac{\sqrt{3}}{2})}^{2} = 1 - 2 \cdot \frac{3}{4} = 1 - \frac{3}{2} = - \frac{1}{2} \neq \frac{1}{2}$ $1 - 2 * (sqrt(3)/2)^2 = 1-2*3/4 = 1-3/2 = -1/2 != 1/2$ //

Which proves it is False

Science

Math

Humanities

... and beyond

How do you prove $sin x = 1 - 2 {cos}^{2} x$ $sin x = 1 - 2 cos^2x$ ?

1 Answer

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you prove sinx=1−2cos2xsin x = 1 - 2 cos^2x?

1 Answer

Related questions

Impact of this question

How do you prove $sin x = 1 - 2 {cos}^{2} x$ $sin x = 1 - 2 cos^2x$ ?