Question

State true or false:

The value of the expression $(sin{80}^0-cos{80}^0)$ is negative.

Answer 1

$\sin 80°-\cos 80°=\sin (90°-10°)-\cos (90°-10°)$

$=\sin 90°\cos 10°-\cos 90°\sin 10°-\cos 90°\cos 10°-\sin 90°\sin 10°$

$=\cos 10°-0-0-\sin 10°$

$=\cos 10°-\sin 10°$

Hence, the answer is $\cos 10°-\sin 10°.$