Sure thing! Here are the steps I took to find the value of con(tan-¹(6/8)):
1. Recall the identity: con(θ) = adj/hyp
2. Draw a right triangle with opposite side of 6 and adjacent side of 8.
3. Use the Pythagorean theorem to find the hypotenuse: hyp² = opp² + adj²
4. hyp² = 6² + 8² = 36 + 64 = 100
5. hyp = √100 = 10
6. Use the identity: tan(θ) = opp/adj
7. tan(θ) = 6/8 = 3/4
8. Take the inverse tangent of both sides: tan-¹(tan(θ)) = tan-¹(3/4)
9. Simplify: θ = tan-¹(3/4)
10. Recall the identity: con(θ) = adj/hyp
11. Substitute adj = 8 and hyp = 10: con(tan-¹(6/8)) = 8/10 = 4/5
So, the value of con(tan-¹(6/8)) is 4/5.