Assertion (A) : $\cos 1 < \cos 2$ 

Reason(R) : In $(0,\mathrm{\pi }), \mathrm{cosx}$ is decreasing function

 

Solution:

The assertion is $\cos 1<\cos 2$

1 means $57.29°$ and it lies in the first quadrant

and 2 means $114.58°$, it lies in the second quadrant.

The cosine function is posiitve in the first quadrant and negative in the second quadrant

hence, $\cos 1<\cos 2$

Therefore, Assertion is True.

To check the reason, consider the graph of the function $y=\cos x$ in the interval $\left(0,2\mathrm{\pi }\right)$

Therefore, Assertion and reason both are correct. and Reason is correct explanation of Assertion.