State whether the following are true or false. Justify your answer that,
$\cos A$ is the abbreviation for the cosecant of angle A.

Hint:The truth value of the given statement is false because $\cos A$ is the abbreviation for cosine of angle A and the abbreviation for the cosecant of angle A is $\csc A$.

Complete step-by-step answer:
We have to state whether this statement” $\cos A$ is the abbreviation for the cosecant of angle A” is true or false.
From the trigonometric functions we know that $\cos A$ is the abbreviation for cosine of angle A.
And the abbreviation for the trigonometric function cosecant of angle A is $\cos ecA\text{ or }\csc A$.
Hence, the statement given in the question is clearly false because we have discussed above that the abbreviation for $\cos A$ is cosine of angle A not cosecant of angle A. We have also shown that the abbreviation for cosecant of angle A is $\cos ecA\text{ or }\csc A$ not $\cos A$.

Note: There is a trick to remember whether $\cos A$ is the abbreviation for cosine of angle A or cosecant of angle A.
As you can see that the three letters of the word “cosine” has $''\cos ''$ in it so we can easily remember that $\cos A$ is the abbreviation for cosine of angle A.
Similarly, you too can remember that the abbreviation for cosecant of angle A is $\cos ecA\text{ or }\csc A$.
As the first five letters of the word “cosecant” contain $''\cos ec''$ in it so we can easily remember the abbreviation for cosecant of angle A and the word “cosecant” also comprises $''\csc ''$.