Answer: the exact value of tan(13π/12) is √3 + 2.
Step-by-step explanation: The trigonometric equation demonstrating the equality between the tangent of 13π/12 and the tangent of 3π/4 added to π/3 may be expressed in the formal and technical tone often employed in academic writing as follows: tan(13π/12) = tan(3π/4 + π/3).
Through utilization of the identity, tan(a+b) = (tan(a) + tan(b)) / (1 - tan(a)*tan(b)), the given expression may be rendered more concise.
The trigonometric expression tan(13π/12) can be represented as (tan(3π/4) + tan(π/3)) divided by (1 - tan(3π/4) multiplied by tan(π/3)).
It is established that:
it can be observed that the value of the trigonometric function of tan(3π/4) is -1.
The mathematical expression "tan(π/3) = √3" signifies that the trigonometric tangent function of the angle π/3 is equivalent to the square root of three.
Upon substitution of the aforementioned values, the resulting output is obtained.
The trigonometric function of tan(13π/12) can be expressed as a quotient between two real numbers. Specifically, it can be represented in the form (-1 + √3) / (1 + (-1) * √3).
By utilizing the conjugate of the denominator and performing the operation of multiplication on both the numerator and denominator, the resulting expression is obtained:
The trigonometric function of tangent evaluated at 13π/12 is expressed as the product of two fractions. The numerator of the first fraction is comprised of the difference of the values -1 and the positive square root of 3, while the denominator is the sum of the value 1 and the product of -1 and the square root of 3. The numerator of the second fraction is the sum of the values 1 and the positive square root of 3, while the denominator is the sum of the same values.
The trigonometric identity expressed as tan(13π/12) has been rendered in symbolic form, wherein the numerator is the summation of -1, √3, √3, and -3. The denominator is the product of (1 + √3) and (1 - √3).
The mathematical expression tan(13π/12) can be represented as (-2√3 - 4) / (-2).
The mathematical expression tan(13π/12) is equivalent to the value of √3 + 2.