Answer:
Explanation:
a. csc(θ) + sec(-θ)
Recall that csc(θ) = 1/sin(θ) and sec(θ) = 1/cos(θ). Also note that sec(-θ) = sec(θ), since the secant function is even.
Therefore,
csc(θ) + sec(-θ) = 1/sin(θ) + 1/cos(θ)
Substituting a for sin(θ) and b for cos(θ), we get:
csc(θ) + sec(-θ) = 1/a + 1/b
To simplify this expression, we can find a common denominator:
csc(θ) + sec(-θ) = (b + a)/(ab)
Therefore, csc(θ) + sec(-θ) = (a + b)/(ab)
b. cot θ - csc θ
Recall that cot(θ) = cos(θ)/sin(θ) and csc(θ) = 1/sin(θ).
Therefore,
cot(θ) - csc(θ) = cos(θ)/sin(θ) - 1/sin(θ)
Substituting a for sin(θ) and b for cos(θ), we get:
cot(θ) - csc(θ) = b/a - 1/a
To simplify this expression, we can find a common denominator:
cot(θ) - csc(θ) = (b - 1)/a
Therefore, cot(θ) - csc(θ) = (b - 1)/a.