Which expression is equivalent to tan theta-sec theta/sin theta?
A)-cot theta
B)cot theta
C)tan theta-cot theta
D)tan theta-sec^2theta
just tell me what I need to know to set it up
trig identities are like in a different language for me. can I please get at least 1 step to get started. I looked at all the sites about it but if I don't understand what im looking at it does no good, I know how to read I just don't get it.
Notation: sin(theta) = s; cos(theta) = c.
Then tan(theta) = s/c and
sec(theta) = 1/c
We can write:
s/c - 1/(cs) = (s^2 - 1)/(cs) = -c/s = Answer A
I understand that a little thank you sooo much for explaining it.
if you ar having issues read it again or 3 times . you can also try to contact a friend
To determine which expression is equivalent to tan theta - sec theta / sin theta, we'll need to simplify the given expression by applying trigonometric identities.
First, let's rewrite the expression:
tan theta - sec theta / sin theta
Next, let's express sec theta as 1/cos theta using the reciprocal identity:
tan theta - 1/cos theta / sin theta
To simplify further, we need to find a common denominator for the terms in the numerator:
tan theta - 1 / cos theta * sin theta
The common denominator for tan theta and 1/cos theta is cos theta. So, multiplying the numerator and denominator of the second term by cos theta:
tan theta - sin theta / cos theta
Now, let's simplify the expression by using the Pythagorean identity: sin^2 theta + cos^2 theta = 1. Dividing the entire expression by cos theta:
tan theta / cos theta - sin theta / cos theta
tan theta / cos theta is equivalent to cot theta:
cot theta - sin theta / cos theta
The term sin theta / cos theta is equivalent to tan theta, so the final simplified expression is:
cot theta - tan theta
Therefore, the answer is option C) tan theta - cot theta.