Question.
State whether the following are true or false. Justify your answer
(i) The value of tan A is always less than 1.
(ii) $\sec A=\frac{12}{5}$ for some value of angle $A$.
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) $\sin \theta=\frac{4}{3}$ for some angle $\theta$.
State whether the following are true or false. Justify your answer
(i) The value of tan A is always less than 1.
(ii) $\sec A=\frac{12}{5}$ for some value of angle $A$.
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) $\sin \theta=\frac{4}{3}$ for some angle $\theta$.
Solution:
(i) False.
We know that $60^{\circ}=\sqrt{\mathbf{3}}>\mathbf{1}$.
(ii) True.
We know that value of $\sec A$ is always $\geq 1$.
(iii) False.
Because cos A is abbreviation used for cosine A.
(iv) False, because cot A is not the product of cot and A.
(v) False, because value of sin cannot be more than 1.
(i) False.
We know that $60^{\circ}=\sqrt{\mathbf{3}}>\mathbf{1}$.
(ii) True.
We know that value of $\sec A$ is always $\geq 1$.
(iii) False.
Because cos A is abbreviation used for cosine A.
(iv) False, because cot A is not the product of cot and A.
(v) False, because value of sin cannot be more than 1.