Question
State whether the following are true or false. Justify your answer.
$\sec\text{A}=\frac{12}{5}$ for some value of angle A.
$\sec\text{A}=\frac{12}{5}$ for some value of angle A.
✓
Answer
$\sec\text{A}=\frac{1}{\cos\text{A}}$
In sec A and $\cos\text{A},\angle\text{A}$ is acute angle
Therefore,
Minimum value $\angle\text{A}$ of is 0° and
Maximum value of $\angle\text{A}$ is 90°
We know that cos 0° = 1 and
cos 90° = 0
Now,
$\sec0^\circ=\frac{1}{\cos0^\circ}$
$=\frac{1}{1}$
Therefore minimum value of sec A is sec 0 ° …… (1)
Now,
$\sec90^\circ=\frac{1}{\cos90^\circ}$
$=\frac{1}{0}$
$=\infty$
Therefore maximum value of sec A is $\sec90^\circ=\infty\ \dots(2)$
Now consider the given value
$\sec\text{A}=\frac{12}{5}$
Here, $\frac{12}{5}=2.4$
This value 2.4 lies in between 1 and $\infty$
Now from equation (1) and (2), we can say that the value $\frac{12}{5}=2.4$ lies in between minimum value of sec A (that is 1) and maximum value of sec A (that is $\infty$)
Hence $\sec\text{A}=\frac{12}{5},$ for some value of angle A is true.
In sec A and $\cos\text{A},\angle\text{A}$ is acute angle
Therefore,
Minimum value $\angle\text{A}$ of is 0° and
Maximum value of $\angle\text{A}$ is 90°
We know that cos 0° = 1 and
cos 90° = 0
Now,
$\sec0^\circ=\frac{1}{\cos0^\circ}$
$=\frac{1}{1}$
Therefore minimum value of sec A is sec 0 ° …… (1)
Now,
$\sec90^\circ=\frac{1}{\cos90^\circ}$
$=\frac{1}{0}$
$=\infty$
Therefore maximum value of sec A is $\sec90^\circ=\infty\ \dots(2)$
Now consider the given value
$\sec\text{A}=\frac{12}{5}$
Here, $\frac{12}{5}=2.4$
This value 2.4 lies in between 1 and $\infty$
Now from equation (1) and (2), we can say that the value $\frac{12}{5}=2.4$ lies in between minimum value of sec A (that is 1) and maximum value of sec A (that is $\infty$)
Hence $\sec\text{A}=\frac{12}{5},$ for some value of angle A is true.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Prove that $\sec ^2 \theta-\cos ^2 \theta=\tan ^2 \theta+\sin ^2 \theta$
→Write the coefficient of the polynomial $p(z) = z^5 - 2z^2 + 4.$
→The diameter of a metallic sphere is equal to $9\ cm$. It is melted and drawn into a long wire of diameter $2\ mm$ having uniform cross-section. Find the length of the wire.
→A study related to time (in months) taken to settle a dispute in a lower court resulted the following data.
Find the mean time taken to settle a dispute in a lower court.
| Time (in months | 0 - 2 | 2 - 4 | 4 - 6 | 6 - 8 | 8 - 10 | 10 -12 |
| No. of disputes | 15 | 90 | 120 | 75 | 70 | 50 |
A box contains 3 apples, 4 oranges and 5 bananas. One fruit is drawn at random from the box. Write $S, n(S)$ and sample points of each of the following events.
Event A: Fruit is orange or banana
Event B: Fruit is not an apple.
Event C: Fruit is neither apple nor banana
Event D : Fruit is banana
→Event A: Fruit is orange or banana
Event B: Fruit is not an apple.
Event C: Fruit is neither apple nor banana
Event D : Fruit is banana
Water flows at the rate of $15km/hr$ through a pipe of diameter $14\ cm$ into a cuboidal pond which is $50\ m$ long and $44\ m$ wide. In what time will the level of water in the pond rise by $21\ cm$?
→Solve : 25x² + 30x + 9 = 0
In the following figure, an equilateral triangle ABC of side 6cm has been inscribed a circle. Find the area of the shaded region. $\big(\text{Take }\pi=3.14\big).$
→The product of two successive integral multiples of $5$ is $300$. Determine the multiples.
→In a trapezium ABCD, it is given that AB || CD and AB = 2CD. Its diagonals AC and BD intersect at the point O such that $\text{ar}(\triangle\text{AOB})=84\text{cm}^2.$ Find $\text{ar}(\triangle\text{COD}).$
→