Final answer:
To simplify (sec t)(tan t)(cos t), rewrite it using trigonometric identities and cancel out the cosine terms, leaving (sin t).
Step-by-step explanation:
To simplify the expression (sec t)(tan t)(cos t), we can rewrite it using trigonometric identities. Recall that secant is the reciprocal of cosine, and tangent is the sine divided by the cosine. Therefore, (sec t)(tan t)(cos t) becomes (1/cos t)(sin t/cos t)(cos t). The cosine terms cancel out, leaving us with (sin t).