Question

Simplify the expression tan(θ−4/π)?

A) tan(θ)−1
B) tan(θ)+1
C) tan(θ)− 1/√2
D) tan(θ)+ 1/√2
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Answer 1

The expression tan(θ - π/4) simplifies to tan(θ) - 1 using the tangent difference identity, provided that tan(θ) is not equal to 1.

Step-by-step explanation:

To simplify the expression tan(θ - π/4), we use the trigonometric identity for the tangent of a difference of two angles:

tan(a ± β) = ​(frac{​tan a + tan β}{1 − tan a × tan β}).

For our specific case where a = θ and β = π/4:

• tan(π/4) is known to be 1.
• Therefore, tan(θ - π/4) = ​(frac{​tan(θ) - 1}{1 + tan(θ) × 1}) = tan(θ) - 1 when tan(θ) is not equal to 1 (to avoid division by zero).

The answer is A) tan(θ) - 1.