Topics

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

The value of \( \Large \cos^{4} \theta - \sin^{4} \theta \)

A) \( \Large \cos^{2} \theta - \sin^{2} \theta \)
B) 1
C) \( \Large 1-2\sin^{2} \theta \)
D) \( \Large 2\sin^{2} \theta - 1 \)

Correct Answer:



C) \( \Large 1-2\sin^{2} \theta \)

Description for Correct answer:
\( \Large \cos^{4} \theta - \sin^{4} \theta = \left(\cos^{2} \theta \right)^{2}- \left(\sin^{2} \theta \right)^{2} \)

=\( \Large \left(\cos^{2} \theta + \sin^{2} \theta \right) \left(\cos^{2} \theta - \sin^{2} \theta \right) \)

= \( \Large \cos^{2} \theta - \sin^{2} \theta \)

=\( \Large 1 - \sin^{2} \theta - \sin^{2} \theta \)

=\( \Large 1 - 2\sin^{2} \theta \)

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

Comments

Similar Questions

1). By using the formula, the value of \( \Large \left(\sin \theta +\cos \theta \right)^{2}+ \left(sin \theta - \cos \theta \right)^{2} \) is

A). 1

B). 2

C). 3

D). 4

2). The value of \( \Large \frac{\cos 15 ^{\circ} }{\sin 75 ^{\circ} } \)

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

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

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

D). 1

3). The value of \( \Large \frac{1}{1+\cos A}+\frac{1}{1-\cos A} \)

A). \( \Large 2\cosh^{2}A \)

B). \( \Large 2\sec^{2}A \)

C). \( \Large 2\cot^{2}A \)

D). \( \Large 2\tan^{2}A \)

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

A). 0

B). 1

C). 2

D). \( \Large \frac{1}{2} \)

5). 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.

6). 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.

7). 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.

8). 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.

9). 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.

10). 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.