- Home
- Standard 10
- Mathematics
8. Introduction to Trigonometry
medium
यदि $\sin \theta+\cos \theta=\sqrt{3}$ है, तो सिद्ध कीजिए कि $\tan \theta+\cot \theta=1$ है।
Option A
Option B
Option C
Option D
Solution
$\sin \theta+\cos \theta=\sqrt{3}$
or $(\sin \theta+\cos \theta)^{2}=3$
or $\sin ^{2} \theta+\cos ^{2} \theta+2 \sin \theta \cos \theta=3$
$2 \sin \theta \cos \theta=2$ $\left[\sin ^{2} \theta+\cos ^{2} \theta=1\right]$
or $\sin \theta \cos \theta=1=\sin ^{2} \theta+\cos ^{2} \theta$
or $1 = \quad \frac{\sin ^{2}\theta + \cos ^{2} \theta}{\sin \theta \cos \theta}$
Therefore $\tan \theta+\cot \theta=1$
Standard 10
Mathematics
