Topics

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

Find the value of \( \Large \frac{2\sin^{2}45-tan^{2}45}{2\tan^{2}45} \)

A) 0
B) 1
C) 2
D) \( \Large \frac{1}{2} \)

Correct Answer:

A) 0

Description for Correct answer:
\( \Large \frac{2\sin^{2}45-\tan^{2}45}{2\tan^{2}45} \)

\( \Large Nr = 2\sin^{2}45 - \tan^{2}45 \)

=\( \Large 2 \left(\frac{1}{\sqrt{2}}\right)^{2}-1 = 2 \times \frac{1}{2}-1 = 0 \)

\( \Large Dr = 2\tan^{2}45=2 \times 1 = 2\)

Therefore, \( \Large \frac{2\sin^{2}45 - \tan^{2}45}{2\tan^{2}45} = \frac{0}{2} = 0 \)

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

Comments

Similar Questions

1). A ladder with length of 24 metres is placed against the wall at an angle of elevation of \( \Large 30 ^{\circ} \). Then the height of the building is

A). 18 mts.

B). 24 mts.

C). 12 mts.

D). 16mts.

2). In \( \Large \triangle ABC,\ m \angle B=90 ^{\circ} ,\ BC=12\ cm.,\ AB=5\ cm. \) using pythogorass property find the value of the hypotenuse?

A). 13 cm.

B). 14 cm.

C). 7 cm.

D). 18 cm.

3). A man sees the bottom of tree from the top of the building whose height is 45 mts. at an angle of depression \( \Large 45 ^{\circ} \). Find the distance between the building and the bottom of the tree.

A). 30 mts.

B). 60 mts.

C). 45 mts.

D). 40 mts.

4). P and Q are the two points on the ground. In between them a pole AB is stood. A is tied to P and A is tied to Q. P makes an angle of \( \Large 30 ^{\circ} \) and Q makes an angle of \( \Large 45 ^{\circ} \), with the ground respectively. The length of PA is 10 mts. Find the length of AQ.

A). \( \Large 10\sqrt{2} \)mts.

B). \( \Large \sqrt{20} \)mts.

C). \( \Large 4\sqrt{5} \)mts.

D). \( \Large 5\sqrt{2} \)mts.

5). A man at a point sees the top of a tower at an angle of elevation \( \Large 30 ^{\circ} \). If he after walking 24 metres from that point towards the tower, the angle of elevation becomes \( \Large 60 ^{\circ} \), then the height of the tower is

A). 12 mts.

B). \( \Large 4\sqrt{3} \)mts.

C). \( \Large 12\sqrt{3} \)mts.

D). none of these.

6). There are two temples on the banks of a river and they are opposite to each other on either side of the river. from the 54' height temple from the top a man sees the top of the other temple at an angle of depression \( \Large 30 ^{\circ} \). and the bottom of the temple at an angle of depression \( \Large 60 ^{\circ} \) respectively. Find the height of the other temple?

A). 36 mts.

B). 40 mts.

C). 42 mts.

D). 54 mts.

7). The height of the two poles are 80 mts. and 62.5 mts. A man stands at the top of long pole sees the top of the small pole at an angle of \( \Large 45 ^{\circ} \). Then the distance between the two poles is.

A). 142.5 mts.

B). 60.5 mts.

C). 17.5 mts.

D). 100 mts.

8). Two ships are on either side of' a light house of height 100 mts. The angle of elevation from the two ships to see the top of the light house are \( \Large 30^{\circ} \) and \( \Large 45 ^{\circ} \) respectively. Then the distance between the two ships is

A). 273 mts.

B). 100 mts.

C). 100 mts.

D). \( \Large 200\sqrt{3} \)mts.

9). The distance between two buildings is 60 mts. A man sees the top of the other building from the height of the building of 150 mts at an angle of depression \( \Large 30^{\circ} \). Then the height of the other building is

A). 115.6 mts.

B). 115.4 mts.

C). 120 mts.

D). 120.64 mts.

10). 5 radian is equal to

A). \( \Large 5 \times \frac{90}{ \pi } ^{\circ} \)

B). \( \Large 5 \times \frac{180}{ \pi } ^{\circ} \)

C). \( \Large 5 \times \frac{270}{ \pi } ^{\circ} \)

D). \( \Large 5 \times \frac{360}{ \pi } ^{\circ} \)