Show $1-\cos \left(2\mathrm{\theta }\right)=2{\sin \left(\mathrm{\theta }\right)}^2$.

Input the expression for the left-hand side.

Tip: Find $\mathrm{\theta }$ in the Greek palette, or type theta and use symbol completion.$$

$1-\cos \left(2\mathrm{\theta }\right)$

Smart popups, if any, are shown at the top of the Context Panel. Each smart popup shows a preview of the result.

Select expand. The result is returned to the worksheet.

From the smart popups for this output, select simplify.

The result is returned to the worksheet.  The identity has been verified.

Apply the double angle identity for $\sin \left(2\mathrm{\theta }\right)$.

Input the expression $\sin \left(2\mathrm{\theta }\right)$.

$\sin \left(2\mathrm{\theta }\right)$

Smart popups are shown at the top of the Context Panel.  Hover your pointer over Trig Identities to see a list of identities.

Select $2\sin \left(\mathrm{\theta }\right)\cos \left(\mathrm{\theta }\right)$. The result is returned to the worksheet.

Input the expression $\cos \left(\frac{1}{10}xy\right)$.

$\cos \left(\frac{1}{10}xy\right)$

Smart popups are shown at the top of the Context Panel.

Select 3D Plot from the available choices. The result is returned to the worksheet.