Answer:
To express cot(theta) and cosec(theta) in terms of cos(theta), we can use the basic trigonometric identities:
1. cot(theta) = 1 / tan(theta) = 1 / (sin(theta) / cos(theta)) = cos(theta) / sin(theta)
2. cosec(theta) = 1 / sin(theta)
Now, let's express cot(theta) and cosec(theta) in terms of cos(theta):
1. cot(theta) = cos(theta) / sin(theta)
Since sin(theta) = 1 / cosec(theta), we can substitute this value in the expression for cot(theta):
cot(theta) = cos(theta) / (1 / cosec(theta))
Now, to divide by a fraction, we can multiply by its reciprocal:
cot(theta) = cos(theta) * cosec(theta)
Now, substituting sin(theta) = 1 / cosec(theta) in the expression for cot(theta):
cot(theta) = cos(theta) * (1 / sin(theta))
Therefore, we have the expressions for cot(theta) and cosec(theta) in terms of cos(theta):
cosec(theta) = 1 / sin(theta)
Step-by-step explanation:
To express cot theta and cosec theta in terms of cos theta, we'll use the following identities:
cot theta = cos theta / sin theta
cosec theta = 1 / sin theta
Using the identity sin^2 theta + cos^2 theta = 1, we can express sin theta in terms of cos theta:
sin theta = sqrt(1 - cos^2 theta)
Now, substituting sin theta in the identities for cot theta and cosec theta, we have:
cot theta = cos theta / sqrt(1 - cos^2 theta)
cosec theta = 1 / sqrt(1 - cos^2 theta)
Therefore, cot theta and cosec theta in terms of cos theta are:
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Answer:
To express cot(theta) and cosec(theta) in terms of cos(theta), we can use the basic trigonometric identities:
1. cot(theta) = 1 / tan(theta) = 1 / (sin(theta) / cos(theta)) = cos(theta) / sin(theta)
2. cosec(theta) = 1 / sin(theta)
Now, let's express cot(theta) and cosec(theta) in terms of cos(theta):
1. cot(theta) = cos(theta) / sin(theta)
2. cosec(theta) = 1 / sin(theta)
Since sin(theta) = 1 / cosec(theta), we can substitute this value in the expression for cot(theta):
cot(theta) = cos(theta) / (1 / cosec(theta))
Now, to divide by a fraction, we can multiply by its reciprocal:
cot(theta) = cos(theta) * cosec(theta)
Now, substituting sin(theta) = 1 / cosec(theta) in the expression for cot(theta):
cot(theta) = cos(theta) * (1 / sin(theta))
Therefore, we have the expressions for cot(theta) and cosec(theta) in terms of cos(theta):
cot(theta) = cos(theta) * cosec(theta)
cosec(theta) = 1 / sin(theta)
Step-by-step explanation:
Answer:
To express cot theta and cosec theta in terms of cos theta, we'll use the following identities:
cot theta = cos theta / sin theta
cosec theta = 1 / sin theta
Using the identity sin^2 theta + cos^2 theta = 1, we can express sin theta in terms of cos theta:
sin theta = sqrt(1 - cos^2 theta)
Now, substituting sin theta in the identities for cot theta and cosec theta, we have:
cot theta = cos theta / sqrt(1 - cos^2 theta)
cosec theta = 1 / sqrt(1 - cos^2 theta)
Therefore, cot theta and cosec theta in terms of cos theta are:
cot theta = cos theta / sqrt(1 - cos^2 theta)
cosec theta = 1 / sqrt(1 - cos^2 theta)