Trigonometric Identities Question 164
Question: What is $ {{\sin }^{2}}(3\pi )+{{\cos }^{2}}(4\pi )+{{\tan }^{2}}(5\pi ) $ equal to?
Options:
A) 0
B) 1
C) 2
D) 3
Show Answer
Answer:
Correct Answer: B
Solution:
$ {{\sin }^{2}}(3\pi )+cos^{2}(4\pi )+{{\tan }^{2}}(5\pi ) $ $ ={{\sin }^{2}}(3\pi )+{{\cos }^{2}}(\pi +3\pi )+{{\tan }^{2}}(5\pi ) $ $ =({{\sin }^{2}}(3\pi )+{{\cos }^{2}}(3\pi )+{{\tan }^{2}}(2\times 2\pi +\pi ) $ $ =1+{{\tan }^{2}}\pi ={{\sec }^{2}}\pi =1 $
BETA
