Topics

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

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 \(^{\circ}\)

Correct Answer:


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

Description for Correct answer:
\( \Large \frac{tan \ 57 ^{\circ} +cot \ 37 ^{\circ} }{tan \ 33 ^{\circ} +cot \ 53 ^{\circ} }=

\frac{tan \ 57 ^{\circ} +cot \ 37 ^{\circ} }{cot \ 57 ^{\circ} +tan \ 37 ^{\circ} } \)

= \( \Large \frac{tan57 ^{\circ} +\frac{1}{tan37 ^{\circ} }}{\frac{1}{tan57 ^{\circ} }+tan37 ^{\circ} } \)

= \( \Large \frac{1+tan57 ^{\circ} tan37 ^{\circ} }{1+tan37 ^{\circ} tan57 ^{\circ} } \times \frac{tan57 ^{\circ} }{tan37 ^{\circ} } \)

= \( \Large \frac{tan57 ^{\circ} }{tan37 ^{\circ} }=tan \ 57 ^{\circ} .\ cot \ 37 ^{\circ} \)

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

Comments

Similar Questions

1). 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

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

A). 2

B). 3

C). 1

D). 4

3). 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)

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

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

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

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

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

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

10). If x=\( \Large a \ sec \theta \ cos \theta ,\ y=b \ sec \theta \ sin \theta \) and z=\( \Large c \ tan \theta \ \), then the value of \( \Large \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}-\frac{z^{2}}{c^{2}} \) is

A). 9

B). 0

C). 1

D). 4