Is cos(x-pi/6)-cos(x+pi/6)=sin(x) ?

The answer to whether cos(x-pi/6)-cos(x+pi/6)=sin(x) is True

Popular >

prove cos(x-pi/6)-cos(x+pi/6)=sin(x)

prove

cos (x - \frac{π}{6}) - cos (x + \frac{π}{6}) = sin (x)

True

Solution steps

cos (x - \frac{π}{6}) - cos (x + \frac{π}{6}) = sin (x)

Manipulating left side

cos (x - \frac{π}{6}) - cos (x + \frac{π}{6})

Rewrite using trig identities

= \frac{3}{2} cos (x) + \frac{1}{2} sin (x) - cos (x + \frac{π}{6})

Rewrite using trig identities

= \frac{3}{2} cos (x) + \frac{1}{2} sin (x) - (\frac{3}{2} cos (x) - \frac{1}{2} sin (x))

Simplify

\frac{3}{2} cos (x) + \frac{1}{2} sin (x) - (\frac{3}{2} cos (x) - \frac{1}{2} sin (x)) : sin (x)

= sin (x)

We showed that the two sides could take the same form

\Rightarrow True

cos (\frac{3 π}{2} + θ) = sin (θ)

csc^{2} (θ) - cos^{2} (θ) csc^{2} (θ) = 1

tan (2 θ) = \frac{2 tan ( θ )}{1 - tan ^{2} ( θ )}

sin^{2} (θ) tan^{2} (θ) = tan^{2} (θ) - sin^{2} (θ)

1 - tan^{2} (x) = 2 - sec^{2} (x)

Is cos(x-pi/6)-cos(x+pi/6)=sin(x) ?
The answer to whether cos(x-pi/6)-cos(x+pi/6)=sin(x) is True