Question : If $\sin\theta +\cos\theta=\sqrt{2}\sin(90^{\circ}-\theta)$, then the value of $\cot\theta$ is:
Option 1: $-\sqrt{2}-1$
Option 2: $\sqrt{2}-1$
Option 3: $\sqrt{2}+1$
Option 4: $-\sqrt{2}+1$
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: $\sqrt{2}+1$
Solution : Given: $\sin\theta +\cos\theta=\sqrt{2}\sin(90^{\circ}-\theta)$ $⇒\sin\theta +\cos\theta=\sqrt{2}\cos\theta$ $⇒\sin\theta=(\sqrt{2}-1)\cos\theta$ $⇒\cot\theta=\frac{1}{\sqrt{2}-1}$ By rationalisation, $\cot\theta=\sqrt{2}+1$ Hence, the correct answer is $\sqrt{2}+1$.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : $\frac{1+\cos \theta-\sin ^2 \theta}{\sin \theta(1+\cos \theta)} \times \frac{\sqrt{\sec ^2 \theta+\operatorname{cosec}^2 \theta}}{\tan \theta+\cot \theta}, 0^{\circ}<\theta<90^{\circ}$, is equal to:
Question : If $0\leq\theta\leq 90^{\circ}$ and $4\cos^{2}\theta-4\sqrt{3}\cos\theta+3=0$, then the value of $\theta$ is:
Question : If $\cos\theta+\sin\theta=\sqrt{2}\cos\theta$, then $\cos\theta-\sin\theta$ is:
Question : If $\cos \theta+\cos ^2 \theta=1$, find the value of $\sqrt{\sin ^4 \theta+\cos ^2 \theta}$.
Question : If $7\sin^{2}\theta+3\cos^{2}\theta=4$, and $0^{\circ}< \theta< 90^{\circ}$, then the value of $\tan\theta$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile