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8. Introduction to Trigonometry
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જો $\sin \theta+\cos \theta=\sqrt{3},$ તો સાબિત કરો કે $\tan \theta+\cot \theta=1$
Option A
Option B
Option C
Option D
Solution
$\sin \theta+\cos \theta=\sqrt{3}$ (આપેલ છે.)
$\therefore$ $(\sin \theta+\cos \theta)^{2}=3$
$\therefore$ $\sin ^{2} \theta+\cos ^{2} \theta+2 \sin \theta \cos \theta=3$
$2 \sin \theta \cos \theta=2$ $\left[\sin ^{2} \theta+\cos ^{2} \theta=1\right]$
$\therefore$ $\sin \theta \cos \theta=1=\sin ^{2} \theta+\cos ^{2} \theta$
$\therefore$ $1 = \quad \frac{\sin ^{2}\theta + \cos ^{2} \theta}{\sin \theta \cos \theta}$
$\therefore$ $\tan \theta+\cot \theta=1$
Standard 10
Mathematics
Similar Questions
જોડકા જોડો.
| $1 .$ $\cos \theta$ | $a.$ $\frac{\cos \theta}{\sin \theta}$ |
| $2.$ $\tan \theta$ | $b.$ $\frac{1}{\operatorname{coses} \theta}$ |
| $3 .$ $\cot \theta$ | $c.$ $\frac{1}{\sec \theta}$ |
| $4.$ $\sin \theta$ | $d.$ $\frac{1}{\cot \theta}$ |
| $e.$ $\sin \theta \cdot \cos \theta$ |
easy
