This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To simplify the expression (^2 t + ^2 t)/^2 t, we will use a fundamental trigonometric identity. Step 1: Apply the Pythagorean identity. The Pythagorean identity states that ^2 t + ^2 t = 1. Substitute this into the numerator of the expression: (^2 t + ^2 t)/(^2 t) = (1)/(^2 t) Step 2: Use the reciprocal identity. The reciprocal identity for sine states that t = (1)/( t). Therefore, ^2 t = ((1)/( t))^2 = (1)/(^2 t). So, the expression simplifies to: (1)/(^2 t) = ^2 t Comparing this result with the given options: A) ^2 t B) ^2 t C) ^2 t D) ^2 t The simplified expression matches option D. The final answer is D) ^2 t.