Question

 Write True' or False' and justify your answer the following :

The value of the expression \[\sin {80}^° - \cos {80}^°\] 

Answer 1

Consider the table. 

θ	0°	30°	45°	60°	90°
sin θ	0	`1/2`	`1/sqrt2`	`sqrt3/2`	1
cos θ	1	`sqrt3/2`	`1/sqrt2`	`1/2`	0

Here, 

`sin 60°-cos 60°=sqrt3/2-1/2>0` 

`sin 90°-cos 90°= 1-0>0 ` 

`so, sin 80°-cos 80° > 0`    ` (sin θ-cos θ≥0AA45°≤ θ ≤ 90° )`

Therefore, the given statement is false.