Final answer:
To find the value of tan11° given that tan1°=a, we use the tangent addition formula. However, to calculate the exact value of tan11°, we need to know tan10°, which is not provided, thus we cannot complete the calculation without additional information or a calculator.
Step-by-step explanation:
If tan1°=a, then to find the value of tan11°, we can make use of the tangent addition formula. This formula from trigonometry is used to express the tangent of the sum of two angles in terms of the tangents of the individual angles. According to the formula given:
tan(a ± β) = \frac{tan a + tan β}{1 - tan a tan β}
Since we want tan11°, we can express it as tan(10° + 1°). Plugging in the values, we have:
tan11° = tan(10° + 1°) = \frac{tan10° + tan1°}{1 - tan10°tan1°}
However, without the value of tan10°, we cannot calculate the exact value of tan11°. Therefore, we can either find tan10° using a calculator, trigonometric tables or relying on an angle addition theorem with known angles. Note that tan1° is given as 'a'.