Question : If $\alpha \sin 45^{\circ}=\beta \operatorname{cosec} 30^{\circ}$, then $\frac{\alpha^4}{ \beta^4}$ is:
Option 1: $4^4$
Option 2: $3^3$
Option 3: $2^3$
Option 4: $4^3$
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: $4^3$
Solution : $\sin 45^{\circ}$ = $\frac{1}{\sqrt2}$ $\operatorname{cosec} 30^{\circ}$ = 2 $\alpha \sin 45^{\circ}=\beta \operatorname{cosec} 30^{\circ}$ ⇒ $\alpha\times{\frac{1}{\sqrt2}}=\beta\times{2}$ ⇒ $\frac{\alpha}{\beta}$ = $2\times{\sqrt{2}}$ $\therefore$ $\frac{\alpha^4}{\beta^4}=(\frac{\alpha}{\beta})^4 = (2\times{\sqrt{2}})^4 = 64 = 4^3$ Hence, the correct answer is $4^3$.
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 $\alpha +\beta =90^{\circ}$, then the expression $\frac{\tan \alpha}{\tan \beta}+\sin^{2}\alpha+\sin^{2}\beta$ is equal to:
Question : If $\frac{\sin \theta}{\cot \theta+\operatorname{cosec} \theta}=1$, then what is the value of $\theta$?
Question : If $\alpha$ and $\beta$ are positive acute angles, $\sin (4\alpha -\beta )=1$ and $\cos (2\alpha +\beta)=\frac{1}{2}$, then the value of $\sin (\alpha +2\beta)$ is:
Question : If $\sin \alpha=\frac12$ and $\sin \beta=\frac12$, then what is the value of $\cos (\alpha+\beta)$? $(0°<\alpha, \beta<90° )$
Question : If $\sin(3\alpha -\beta )=1$ and $\cos(2\alpha+\beta)=\frac{1}{2}$, then the value of $\tan \alpha$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile