If tan A + cot A = 2, then find the value of tan² A + cot² A.
Correct: C
Given tan A + cot A = 2.
Square both sides of the equation: (tan A + cot A)² = 2².
Expand the left side: tan² A + cot² A + 2(tan A)(cot A) = 4.
We know that tan A = 1/cot A, so tan A * cot A = 1.
Substitute this into the equation: tan² A + cot² A + 2(1) = 4.
So, tan² A + cot² A + 2 = 4.
Subtract 2 from both sides: tan² A + cot² A = 4 - 2 = 2.