#### The value of the expression (sin 80° – cos80°) is negative.

Solution.     (sin 80° – cos 80°)
We know that from 0 to 90° sin$\theta$  and cos$\theta$  both are positive i.e.
$0< \sin \theta \leq 90^{\circ}$  (always positive)
$0< \cos \theta \leq 90^{\circ}$ (always positive)
At 45° both the values of sin$\theta$  and cos$\theta$  are the same but after 45° to 90° value of sin is greater than the value of cos$\theta$ Hence sin 80° > cos 80°.
If we subtract a smaller term from bigger than the result is positive.
Hence (sin 80° – cos80°) > 0
So, the given statement is false