Question

standard 16 homework
score: 9/23 answered: 7/16
question 8
simplify the following expression to a single trig function with no fractions.
\\(\frac{1 + \tan(t)}{1 + \cot(t)} = \\)
question help: video message instructor

Explanation:

Step1: Recall cotangent identity

Recall that \(\cot(t)=\frac{1}{\tan(t)}\). Substitute this into the denominator.
The denominator \(1 + \cot(t)\) becomes \(1+\frac{1}{\tan(t)}=\frac{\tan(t)+1}{\tan(t)}\).

Step2: Substitute and simplify

Now the original expression \(\frac{1 + \tan(t)}{1+\cot(t)}\) is \(\frac{1 + \tan(t)}{\frac{\tan(t)+1}{\tan(t)}}\).
Dividing by a fraction is multiplying by its reciprocal, so this is \((1 + \tan(t))\times\frac{\tan(t)}{\tan(t)+1}\).
The \((1 + \tan(t))\) terms cancel out (assuming \(\tan(t)
eq - 1\) to avoid division by zero), leaving \(\tan(t)\).

Answer:

\(\tan(t)\)