Question : If $\sin (\theta +18^{\circ})=\cos 60^{\circ}(0< \theta < 90^{\circ})$, then the value of $\cos 5\theta$ is:
Option 1: $\frac{1}{2}$
Option 2: $0$
Option 3: $\frac{1}{\sqrt{2}}$
Option 4: $1$
New: SSC CHSL tier 1 answer key 2024 out | 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: $\frac{1}{2}$
Solution : $\sin (\theta +18^{\circ})=\cos 60^{\circ}$ We know that $\cos (90^{\circ}-\theta)=\sin\theta$ $⇒\sin (\theta +18^{\circ})=\cos(90^{\circ}-30^{\circ})$ $⇒\sin (\theta +18^{\circ})=\sin30^{\circ}$ $⇒\theta +18^{\circ}=30^{\circ}$ $⇒\theta=12^{\circ}$ $\therefore \cos 5\theta=\cos 5×12^{\circ}=\cos 60^{\circ}=\frac{1}{2}$ Hence, the correct answer is $\frac{1}{2}$.
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 $4\sin^{2}\theta-1=0$ and angle $\theta$ is less then $90^{\circ}$, the value of $\cos^{2}\theta+\tan^{2}\theta$ is: (Take $0^{\circ}< \theta< 90^{\circ}$)
Question : If $\sin 2\theta=\frac{\sqrt{3}}{2}$, then the value of $\sin 3\theta$ is equal to $(0^{\circ}\leq \theta\leq 90^{\circ})$:
Question : If $0^{\circ} < \theta < 90^{\circ}$ and $2 \sin^{2}\theta +3\cos\theta =3$, then the value of $\theta$ is:
Question : If $(4 \sin \theta+5 \cos \theta)=3$, then the value of $(4 \cos \theta-5 \sin \theta)$ is:
Question : If $\cos A+\sin A=\sqrt{2}\cos A$, then $\cos A-\sin A$ is equal to: (where $0^{\circ}< A< 90^{\circ}$)
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile