Question : If $\theta$ is a positive acute angle and $\tan2\theta \tan3\theta=1$, then the value of $2(\cos^2\frac{5\theta}{2}-1)$ is:
Option 1: $-\frac{1}{2}$
Option 2: -1
Option 3: 0
Option 4: $\frac{1}{2}$
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: 0
Solution : Given: $\tan2\theta \tan3\theta=1$ or, $\tan2\theta=\cot3\theta$ or, $\tan2\theta=\tan(90-3\theta)$ or, $2\theta=90-3\theta$ or, $5\theta =90$ $\therefore \theta=18°$ $2(\cos^2\frac{5\theta}{2}-1)$ = $2(\cos^2\frac{5×18°}{2}-1)$ = $2(\cos^245°-1)$ = $2×((\frac{1}{\sqrt{2}})^2-1)$ = $2×-\frac{1}{2}$ = $-1$ Hence, the answer is -1.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : If $\sec\theta-\cos\theta=\frac{3}{2}$, where $\theta$ is a positive acute angle, then the value of $\sec\theta$ is:
Question : If $\tan\theta-\cot\theta=0$ and $\theta$ is positive acute angle, then the value of $\frac{\tan(\theta+15)}{\tan(\theta-15)}$ is:
Question : If $\sec \theta-2 \cos \theta=\frac{7}{2}$, where $\theta$ is a positive acute angle, then the value of $\sec \theta$ is:
Question : If $\theta$ is a positive acute angle and $4\sin^{2}\theta =3$, then the value of $\left (\tan\theta-\cot\frac{\theta}{2}\right)$ is:
Question : $\theta$ is a positive acute angle and $\sin\theta-\cos\theta=0$, then the value of $\sec\theta+\operatorname{cosec}\theta$ is:
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile