Evaluate the product (log tan 1°) (log tan 2°) … (log tan 50°).

Introduction / Context:Among well-known trigonometric values, tan 45° = 1, so log(tan 45°) = log 1 = 0 (for any base). Because the product explicitly includes the factor with 45°, the entire product collapses to zero.

Given Data / Assumptions:

• Sequence runs from 1° up to 50°; thus it includes 45°.
• All logs share the same base.

Concept / Approach:

• Multiplying any finite product by 0 yields 0.
• No other special pairing is required, though identities like tan θ · tan(90° − θ) = 1 can explain complementary behavior.

Step-by-Step Reasoning:

Verification / Alternative check:Countrate the terms: 1°, 2°, …, 45°, …, 50° includes 45°; hence result is immediate.

Why Other Options Are Wrong:

• 1, 2, −1 ignore the zero factor.

Common Pitfalls:

• Confusing “product of logs” with “log of product”. Here we are literally multiplying log values.

Final Answer:0