Final answer:
The trigonometric identity that is equivalent to 1−cosθ+cosθ is 2cos^2θ (option A).
Step-by-step explanation:
The trigonometric identity that is equivalent to 1−cosθ+cosθ is 2cos^2θ (option A).
To see why, we can simplify the expression 1−cosθ+cosθ. Notice that the terms -cosθ and +cosθ cancel each other out, leaving just 1. Therefore, the expression simplifies to 1, which is equal to cos^2θ + sin^2θ. Since cos^2θ + sin^2θ is equal to 2cos^2θ when simplified, the equivalent trigonometric identity is 2cos^2θ (option A).