You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.
system
<image>Consider a nonlinear inductor which is defined by $\phi = i + tanh (i)$. Let the current through this inductor be i(t) = sin t. Find the voltage across it (see <image 1>).
A. $[1 + sech^2 (sin t)] cos t$
B. $[1 + sech^2 (sin t)] sin t$
C. $[1 - sech^2 (sin t)] sin t$
D. $[1 - sech^2 (cos t)] sin t$

Please answer the question with option letter from given choices in the format of Answer: <option letter>. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
user
A
Consider a nonlinear inductor which is defined by $\phi = i + tanh (i)$. Let the current through this inductor be i(t) = sin t. Find the voltage across it (see <image 1>).
A. $[1 + sech^2 (sin t)] cos t$
B. $[1 + sech^2 (sin t)] sin t$
C. $[1 - sech^2 (sin t)] sin t$
D. $[1 - sech^2 (cos t)] sin t$

Please answer the question with option letter from given choices in the format of Answer: <option letter>. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
val