Question : If $\sin \theta+\cos \theta=\frac{\sqrt{11}}{3}$, then the value of $(\cos \theta-\sin \theta)$ is:
Option 1: $\frac{\sqrt{5}}{3}$
Option 2: $\frac{7}{3}$
Option 3: $\frac{5}{3}$
Option 4: $\frac{\sqrt{7}}{3}$
Correct Answer: $\frac{\sqrt{7}}{3}$
Solution : $\sin \theta+\cos \theta=\frac{\sqrt{11}}{3}$ Squaring, $(\sin \theta+\cos \theta)^2=(\frac{\sqrt{11}}{3})^2$ ⇒ $\sin^2 \theta + \cos^2 \theta + 2\sin \theta \cos \theta = \frac{11}{9}$ ⇒ $1+2\sin \theta \cos \theta = \frac{11}{9}$ ⇒ $2\sin \theta \cos \theta = \frac{11-9}{9}$ ⇒ $2\sin \theta \cos \theta = \frac{2}{9}$ -----------(1) $(\cos \theta-\sin \theta)^2$ $= \sin^2 \theta + \cos^2 \theta - 2\sin \theta \cos \theta $ $= 1-2\sin \theta \cos \theta$ $=1-\frac{2}{9}$ $=\frac{7}{9}$ $\cos \theta-\sin \theta = \sqrt{\frac{7}{9}} = \frac{\sqrt7}{3}$ Hence, the correct answer is $ \frac{\sqrt7}{3}$.
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Question : If $\sin \theta+\cos \theta=\frac{\sqrt{11}}{3}$, then what is $\sin \theta-\cos \theta$?
Question : If $\operatorname{cos} \theta+\operatorname{sin} \theta=\sqrt{2} \operatorname{cos} \theta$, find the value of $(\cos \theta-\operatorname{sin} \theta)$
Question : If $\sin \theta+\cos \theta=\sqrt{2} \cos \theta$, then find $\frac{\sin \theta-\cos \theta}{\sin \theta}$:
Question : If $\frac{\cos \theta}{1-\sin \theta}+\frac{\cos \theta}{1+\sin \theta}=4,0^{\circ}<\theta<90^{\circ}$, then what is the value of $(\sec \theta+\operatorname{cosec} \theta+\cot \theta) ?$
Question : If $4-2 \sin ^2 \theta-5 \cos \theta=0,0^{\circ}<\theta<90^{\circ}$, then the value of $\cos \theta-\tan \theta$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile