Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

If \( \Large tan \ 7 \theta \ tan \ 2 \theta=1 \),then the value of \( \Large tan \ 3 \theta \) is

A) \( \Large \sqrt{3} \)
B) \( \Large -\frac{1}{\sqrt{3}} \)
C) \( \Large \frac{1}{\sqrt{3}} \)
D) \( \Large -\sqrt{3} \)

Correct Answer:



C) \( \Large \frac{1}{\sqrt{3}} \)

Description for Correct answer:
Given, \( \Large tan \ 7 \theta .tan \ 2 \theta =1 \)

=> \( \Large tan7 \theta =cot2 \theta \)

=> \( \Large tan7 \theta =tan(90 ^{\circ} -2 \theta ) \)

=> \( \Large 7 \theta =90 ^{\circ} -2 \theta \)

=> \( \Large 9 \theta =90 ^{\circ} \) => \( \Large \theta =10 ^{\circ} \)

\( \Large tan3 \theta =tan \ 30 ^{\circ} =\frac{1}{\sqrt{3}} \)

Part of solved Trigonometry questions and answers : >> Elementary Mathematics >> Trigonometry

Comments

Similar Questions

1). The expression \( \Large \frac{tan 57 ^{\circ} +cot 37 ^{\circ} }{tan 33 ^{\circ} + cot 53 ^{\circ} } \) is equal to

A). tan 33 \(^{\circ}\) cot 57\(^{\circ}\)

B). tan 57 \(^{\circ}\)cot 37 \(^{\circ}\)

C). tan 33 \(^{\circ}\)cot 53 \(^{\circ}\)

D). tan 53 \(^{\circ}\) cot 37 \(^{\circ}\)

2). The numerical value of \( \Large \frac{5}{sec^{2} \theta }+\frac{2}{1+cot^{2} \theta }+3 \ sin^{2} \theta \) is

A). 5

B). 2

C). 3

D). 4

3). The value of tan 4\(^{\circ}\).tan 43\(^{\circ}\).tan 47 \(^{\circ}\).tan 86 \(^{\circ}\) is

A). 2

B). 3

C). 1

D). 4

4). Consider the following equations

\( \Large cosec^{2}x+sec^{2}x=cosec^{2}x \ sec^{2}x \)

\( \Large sec \ x+tan^{2}x=sec \ x \ tan^{2}x \)

\( \Large cosec \ x+tan^{2}x=cot^{2}x+sec \ x \)

Which of the above equations are correct?

A). (i) and (ii)

B). (ii) and (iii)

C). (i) and (iii)

D). (i), (ii) and (iii)

5). If \( \Large \frac{cos \ x}{1+cosec \ x}+\frac{cosx}{cosec\ x-1}=2 \) ,which one of the following is one of the value of x ?

A). \( \Large \frac{ \pi }{2} \)

B). \( \Large \frac{ \pi }{3} \)

C). \( \Large \frac{ \pi }{4} \)

D). \( \Large \frac{ \pi }{6} \)

6). \( \Large \frac{cos \theta }{1-sin \theta }-\frac{cos \theta }{1+sin \theta }=2 \),is satisfied by which one of the following values of \( \Large \theta \)?

A). \( \Large \frac{ \pi }{2} \)

B). \( \Large \frac{ \pi }{3} \)

C). \( \Large \frac{ \pi }{4} \)

D). \( \Large \frac{ \pi }{6} \)

7). What is \( \Large \sqrt{\frac{1+sin \theta }{1-sin \theta }} \) equal to?

A). \( \Large sec \theta -tan \theta \)

B). \( \Large sec \theta +tan \theta \)

C). \( \Large cosec \theta +cot \theta \)

D). \( \Large cosec \theta -cot \theta \)

8). If \( \Large 7cos^{2} \theta+3sin^{2} \theta =4 \ and \ 0 \ < \ \theta \ < \frac{ \pi }{2} \), what is the value of \( \Large tan \theta \)?

A). \( \Large \sqrt{7} \)

B). \( \Large \frac{7}{3} \)

C). 3

D). \( \Large \sqrt{3} \)

9). The value of \( \Large \frac{tan \ 27 ^{\circ} +cot \ 63 ^{\circ} }{tan \ 27 ^{\circ} (sin \ 25 ^{\circ} +cos \ 65 ^{\circ} )} \)

A). cosec 25 \(^{\circ}\)

B). 2 tan27\(^{\circ}\)

C). sin 25 \(^{\circ}\)

D). tan 65 \(^{\circ}\)

10). If \( \Large cos \theta \ge \frac{1}{2} \) in the first quadrant, which one of the following is correct?

A). \( \Large \theta \le \frac{ \pi }{3} \)

B). \( \Large \theta \ge \frac{ \pi }{3} \)

C). \( \Large \theta \le \frac{ \pi }{6} \)

D). \( \Large \theta \ge \frac{ \pi }{6} \)