Question

standard 16 homework
score: 3/23 answered: 2/16
question 3
simplify the following expression to a single trig function with no fractions.
\\(\frac{\csc(t)}{\cot(t)}\\) =
question help: video message instructor post to forum

Explanation:

Step1: Recall trigonometric identities

Recall that \(\csc(t)=\frac{1}{\sin(t)}\) and \(\cot(t)=\frac{\cos(t)}{\sin(t)}\).

Step2: Substitute identities into the expression

Substitute these into \(\frac{\csc(t)}{\cot(t)}\):

$$ \frac{\frac{1}{\sin(t)}}{\frac{\cos(t)}{\sin(t)}} $$

Step3: Simplify the complex fraction

When dividing by a fraction, multiply by its reciprocal:

$$ \frac{1}{\sin(t)}\times\frac{\sin(t)}{\cos(t)} $$

The \(\sin(t)\) terms cancel out, leaving \(\frac{1}{\cos(t)}\), which is \(\sec(t)\).

Answer:

\(\sec(t)\)