Question : If $7\sin^2\ \theta+3\cos^2\ \theta=4, (0°<\theta<90°)$, then find the value of $\tan\theta$:
Option 1: $\frac{1}{\sqrt3}$
Option 2: $\frac{1}{2}$
Option 3: $1$
Option 4: $\sqrt3$
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $\frac{1}{\sqrt3}$
Solution : Given: $7\sin^2\ \theta+3\cos^2\ \theta=4, (0°<\theta<90°)$ We know the trigonometric identity, $\sin^2\ \theta+\cos^2\ \theta=1$ $3\sin^2\ \theta+3\cos^2\ \theta+4\sin^2\theta=4$ $⇒3(\sin^2\ \theta+\cos^2\ \theta)+4\sin^2\theta=4$ $⇒3+4\sin^2\theta=4$ $⇒4\sin^2\theta=1$ $⇒\sin^2\theta=\frac{1}{4}$ $⇒\sin\ \theta=\frac{1}{2}=\sin \ 30°$ $⇒\theta=30°$ So, the value of $\tan\ \theta$ is, $\tan 30°=\frac{1}{\sqrt3}$ Hence, the correct answer is $\frac{1}{\sqrt3}$.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : If $7\sin^{2}\theta+3\cos^{2}\theta=4$, and $0^{\circ}< \theta< 90^{\circ}$, then the value of $\tan\theta$ is:
Question : If $0°<A<90°$, the value of $\frac{\tan A\ -\ \sec A\ -\ 1}{\tan A\ +\ \sec A\ +\ 1}$ is:
Question : If $r\sin\theta=\frac{7}{2}$ and $r\cos\theta=\frac{7\sqrt3}{2}$, then the value of $\theta$ is:
Question : If $3 \tan \theta=2 \sqrt{3} \sin \theta, 0^{\circ}<\theta<90^{\circ}$, then the value of $\frac{\operatorname{cosec}^2 2 \theta+\cot ^2 2 \theta}{\sin ^2 \theta+\tan ^2 2 \theta}$ is:
Question : If $\tan\theta=1$, then the value of $\frac{8\sin\theta\:+\:5\cos\theta}{\sin^{3}\theta\:–\:2\cos^{3}\theta\:+\:7\cos\theta}$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile