Simplify $\frac{1+\cos (t)}{1+\sec (t)}$ to a single trigonometric ratio with no fractions.
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∻Solution by Steps∻ ‖ step 1 ⋮ Simplify $\frac{1 + \cos(t)}{1 + \sec(t)}$ ‖ ‖ step 2 ⋮ Recall that $\sec(t) = \frac{1}{\cos(t)}$ ‖ ‖ step 3 ⋮ Substitute $\sec(t)$ into the expression: $\frac{1 + \cos(t)}{1 + \frac{1}{\cos(t)}}$ ‖ ‖ step 4 ⋮ Simplify the denominator: $1 + \frac{1}{\cos(t)} = \frac{\cos(t) + 1}{\cos(t)}$ ‖ ‖ step 5 ⋮ Rewrite the expression: $\frac{1 + \cos(t)}{\frac{\cos(t) + 1}{\cos(t)}}$ ‖ ‖ step 6 ⋮ Simplify the fraction: $\frac{(1 + \cos(t)) \cdot \cos(t)}{\cos(t) + 1}$ ‖ ‖ step 7 ⋮ Notice that $(1 + \cos(t))$ cancels out: $\cos(t)$ ‖ ∻Answer∻ ⚹ $\cos(t)$ ⚹ ∻Key Concept∻ ⚹Trigonometric Simplification⚹ ∻Explanation∻ ⚹The given expression simplifies to $\cos(t)$ by substituting $\sec(t)$ and simplifying the resulting fraction.⚹◊What is the difference between cosine and secant in terms of trigonometric ratios?⍭ Generate me a similar question◊

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