Question : If $\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}=3$, then the value of $\sin^{4}\theta$ is:
Option 1: $\frac{2}{5}$
Option 2: $\frac{1}{5}$
Option 3: $\frac{16}{25}$
Option 4: $\frac{3}{5}$
New: SSC CHSL Tier 2 answer key released | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $\frac{16}{25}$
Solution : Given that $\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}=3$ $\frac{\sin\theta+\cos\theta}{\sin\theta-\cos\theta}=\frac{3}{1}$ Applying Componendo and Dividendo, $⇒\frac{2\sin\theta}{2\cos\theta} = \frac{4}{2}$ $⇒\frac{\sin\theta}{\cos\theta} = 2$ $⇒\tan\theta = \frac{2}{1}$ We know that, $\tan\theta =\frac{\text{Perpendicular}}{\text{Base}}$ Let be perpendicular = $2k$, and base = $k$. Using Pythagoras theorem, hypotenuse = $\sqrt{(2k)^2+k^2}=\sqrt5k$ $\sin\theta =\frac{2}{\sqrt5}$ ⇒ $\sin^{4}\theta=(\frac{2}{\sqrt5})^4=\frac{16}{25}$ Hence, the correct answer is $\frac{16}{25}$.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : If $\frac{\sin \theta-\cos \theta}{\sin \theta+\cos \theta}=\frac{4}{5}$, then the value of $\frac{\operatorname{cosec}^2 \theta}{2-\operatorname{cosec}^2 \theta}$ is:
Question : If $\sin \theta-\cos \theta=\frac{1}{5}$, then find the value of $\sin \theta+\cos \theta$.
Question : If $5\tan\theta=4$, then $\frac{5\sin\theta-3\cos\theta}{5\sin\theta+2\cos\theta}$ is equal to:
Question : If $\sin \theta \cos \theta=\frac{1}{\sqrt{3}}$ then the value of $\left(\sin ^4 \theta+\cos ^4 \theta\right)$ is:
Question : If $\sin \theta \cos \theta=\frac{\sqrt{2}}{3}$,then the value of $\left(\sin ^6 \theta+\cos ^6 \theta\right)$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile