# Ex.8.1 Q11 Introduction to Trigonometry Solution - NCERT Maths Class 10

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## Question

(i) The value of $$\text{tan}\,A$$ is always less than $$1.$$

(ii) \begin{align}\text{sec}A=\frac{\text{12}}{\text{5}}\end{align} for some value of $$\angle A$$.

(iii) $$\text{cos}\,A$$ is the abbreviation used for the cosecant of $${\angle A}$$

(iv) $$\text{cot}\, A$$ is the product of $$\rm{cot}$$ and $${A.}$$

(v) \begin{align}\sin \,\theta =\frac{4}{3},\end{align} for some \begin{align}\angle \theta\end{align}

## Text Solution

#### Steps:

(i) False, because sides of a right-angled triangle may have any length. So $$\text{tan}\,A$$ may have any value.

(ii) \begin{align}\text{sec}\,{A=}\,\frac{\text{hypotenuse}}{\text{side}\ \text{adjacent}\ \text{to}\ \angle {A}}\end{align}

As hypotenuse is largest side, the ratio on RHS will be greater than 1. Hence \begin{align}\text{sec }\text{A}>1.\end{align} Thus, the given statement is true.

(iii) Abbreviation used for cosecant of $$\angle A$$ is $$\text{cosec}\,A$$ and $$\text{cos}\,A$$ is the abbreviation used for cosine of $$\rm \angle A$$. Hence the given statement is false.

(iv) $$\text{cot}\,A$$ is not the product of $$\rm{cot}$$ and $${A.}$$ It is the cotangent of $$\rm \angle A$$ . Hence, the given statement is false.

(v)\begin{align}\text{Sin}\,\theta =\frac{4}{3}\end{align}

We know that in a right-angled triangle,

\begin{align}\text{Sin}\,\theta =\frac{\text{side}\ \text{adjacent}\ \text{to}\ \angle \theta }{\text{hypotenuse}}\end{align}

In a right-angled triangle, hypotenuse is always greater than the remaining two sides. Also, the value of Sine should be less than $$1.$$ Therefore, such value of $$\rm{Sin\, \theta}$$ is not possible. Hence the given statement is false.

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