Question

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

• A. True
• B. False
• C. Ambiguous
• D. Data insufficient
  

Answer 1

The correct option is B False

Multiplying and dividing by $\sqrt{2}$
$=\sqrt{2}(\frac{sin{80}^0}{\sqrt{2}}-\frac{cos{80}^0}{\sqrt{2}})$
$=\sqrt{2}\left[sin\right({80}^0-{45}^0\left)\right]$
$=\sqrt{2}sin{35}^0$
Hence False.
Alternatively,
$sin\theta$ increases as $\theta$ increases.
While $cos\theta$ decreases as $\theta$ increases. for $0\le \theta \le {90}^0$
Hence the answer will be false.