Topics

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

If \( \Large tan \theta =\frac{4}{3} \) then the value of \( \Large \frac{3 \ sin \theta +2 \ cos \theta }{3 \ sin \theta -2 \ cos \theta } \) is

A) 0.5
B) -0.5
C) 3
D) -3

Correct Answer:



C) 3

Description for Correct answer:
\( \Large tan \theta =\frac{4}{3} \)

\( \Large \frac{3 \ sin \theta +2 \ cos \theta }{3 \ sin \theta -2 \ cos \theta }=\frac{3 \ tan \theta +2}{3 \ tan \theta -2} \)

\( \Large \frac{3 \times \frac{4}{3}+2}{3 \times \frac{4}{3}-2} =\frac{4+2}{4-2}=3 \)

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

Comments

Similar Questions

1). If \( \Large sec \theta -cosec \theta =0 \), then the value of \( \Large tan \theta +cot \theta \) is

A). 0

B). 1

C). -1

D). 2

2). 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). \( \Large -\sqrt{3} \)

3). 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 \(^{\circ}\)

4). 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

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

A). 2

B). 3

C). 1

D). 4

6). 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)

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

8). \( \Large \frac{cos \theta }{1-sin \theta }-\frac{cos \theta }{1+sin \theta }=2 \),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). \( \Large \frac{ \pi }{6} \)

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

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