Trig Identity & Logarithms Step by step Solution with Explanation

Your question:

1. Write the following in terms of sin e and cos θ; then simplify if possible. (Leave your answer in terms of sin θ and/or cos θ.) csc θ tan θ

2. Use properties of logarithms to expand the logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if po log

Trig Identity & Logarithms Answers and Explanation

Substituting these identities:

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

Therefore, csc(θ) tan(θ) = sin(θ) / cos(θ), which is also equivalent to tan(θ) sec(θ) using another trigonometric identity (sec(θ) = 1 / cos(θ)).

2. Expanding Logarithmic Expressions (Not provided in the prompt)

Evaluating Logarithmic Expressions (Not provided in the prompt)

If you have a specific logarithmic expression to evaluate without a calculator, you can use the following identities:

log_10(100) = log_10(10^2) = 2 * log_10(10) = 2 * 1 (since log_10(10) = 1)

Therefore, log_10(100) = 2.