Write 'True' or 'False' and justify your answer in each of the following:
The value of the expression $ \left(\sin 80^{\circ}-\cos 80^{\circ}\right) $ is negative.

Given:

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

To do:

We have to find whether the given statement is true or false.

Solution:

We know that,

$\sin \theta$ is increasing when, $0^{\circ}<\theta<90^{\circ}$ and $\cos \theta$ is decreasing when $0^{\circ}<\theta<90^{\circ}$.

Therefore,

$sin \( 80^{\circ}-\cos 80^{\circ}>0$

The given statement is false.

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Updated on: 10-Oct-2022

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