For all 0, sin0 + sin(-0) + cos0 + cos(-0) + tan0 + tan(-0) =?
A. 2Sin0
B. 2cos0
C. 2tan0
D. 2sin0 tan0
Correct Answer: B
Explanation
Let's break down the expression:
For \( \theta = 0 \):
- \( \sin(0) = 0 \)
- \( \sin(-0) = \sin(0) = 0 \) (since sine is an odd function)
- \( \cos(0) = 1 \)
- \( \cos(-0) = \cos(0) = 1 \) (since cosine is an even function)
- \( \tan(0) = 0 \)
- \( \tan(-0) = \tan(0) = 0 \) (since tangent is an odd function)
Substitute these values into the expression:
\[
\sin(0) + \sin(-0) + \cos(0) + \cos(-0) + \tan(0) + \tan(-0)
\]
\[
= 0 + 0 + 1 + 1 + 0 + 0
\]
\[
= 2
\]
So the expression simplifies to \(2 \cos(0)\), where \(\cos(0) = 1\).
Thus, the correct answer is:
B. 2 cos(0)