Question

Csc/cot Rewrite in terms of sine and cosine.

a) 1/sin
b) sin/cos
c) cos/sin
d) sin/cos
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Answer 1

The expression csc/cot can be rewritten in terms of sine and cosine as 1/cosine, matching option (c) cos/sin, by using the reciprocal identities of trigonometric functions. csc/cot = 1/cos(θ)

Step-by-step explanation:

To rewrite csc/cot in terms of sine and cosine, we need to recall the definitions of the cosecant (csc) and cotangent (cot) functions in terms of sine and cosine. The cosecant function is the reciprocal of the sine function (csc(θ) = 1/sin(θ)), and the cotangent function is the reciprocal of the tangent function, which itself is the quotient of sine over cosine (cot(θ) = cos(θ)/sin(θ)). Therefore, we can rewrite the given expression as follows:

csc/cot = csc(θ) / cot(θ)

Replacing the functions with their definitions gives us:

csc/cot = (1/sin(θ)) / (cos(θ)/sin(θ))

By multiplying the numerator by the reciprocal of the denominator, the expression simplifies to:

csc/cot = (1/sin(θ)) * (sin(θ)/cos(θ))

The sin(θ) terms cancel out, leaving us with:

csc/cot = 1/cos(θ)