Question
If $3 \sin \theta = 4 \cos \theta,$ then $sec \theta = ?$
✓
Answer
$ 3 \sin \theta=4 \cos \theta \quad \ldots . . \text { [Given] }$
$\therefore \frac{\sin \theta}{\cos \theta}=\frac{4}{3}$
$\therefore \tan \theta=\frac{4}{3} $
We know that,
$1+\tan ^2 \theta=\sec ^2 \theta$
$\therefore 1+\left(\frac{4}{3}\right)^2=\sec ^2 \theta$
$\therefore 1+\frac{16}{9}=\sec ^2 \theta$
$\therefore \sec ^2 \theta=\frac{9+16}{9}$
$\therefore \sec ^2 \theta=\frac{25}{9}$
$\therefore \sec \theta=\frac{5}{3}$ [Taking square root of both sides]
$\therefore \frac{\sin \theta}{\cos \theta}=\frac{4}{3}$
$\therefore \tan \theta=\frac{4}{3} $
We know that,
$1+\tan ^2 \theta=\sec ^2 \theta$
$\therefore 1+\left(\frac{4}{3}\right)^2=\sec ^2 \theta$
$\therefore 1+\frac{16}{9}=\sec ^2 \theta$
$\therefore \sec ^2 \theta=\frac{9+16}{9}$
$\therefore \sec ^2 \theta=\frac{25}{9}$
$\therefore \sec \theta=\frac{5}{3}$ [Taking square root of both sides]
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
In figure 3.80, if PQ = 6, QR = 10, PS = 8 find TS.
If $\sin \theta = \cos (\theta − 45^\circ),$ where $\theta$ and $\theta-45^\circ$ are acute angles, find the degree measure of $\theta.$
→The area of a sector of a circle of radius 2cm is $\pi\text{cm}^2.$ Find the angle contained by the sector.
→Solve the following examples.
Do sides 7 cm , 24 cm, 25 cm form a right angled triangle ? Give reason.
Do sides 7 cm , 24 cm, 25 cm form a right angled triangle ? Give reason.
A die is thrown once. What is the probability of getting a number greater than 4?
Find the first term and common difference for each of the A.P.
$0.6, 0.9, 1.2, 1.5, . . .$
→$0.6, 0.9, 1.2, 1.5, . . .$
Find the first term and common difference for each of the A.P.
$\frac{1}{4}, \frac{3}{4}, \frac{5}{4}, \frac{7}{4}, \ldots$
→$\frac{1}{4}, \frac{3}{4}, \frac{5}{4}, \frac{7}{4}, \ldots$
Which of the following are quadratic equations?
$2\text{x}^2-\sqrt{3}\text{x}+9=0$
→$2\text{x}^2-\sqrt{3}\text{x}+9=0$
The minute hand of a clock is 12cm long. Find the area swept by in it 35 minutes.
Solve the following simultaneous equation.
$3a + 5b = 26; a + 5b = 22$
→$3a + 5b = 26; a + 5b = 22$