How do you simplify this trigonometric expression?

csc(α)

Step-by-step explanation:

We are given .

One key trick when dealing with trig is to write all the functions in terms of cosine and sine.

Tangent (tan) is sine / cosine, secant (sec) is 1 / cosine. So, replace these:

In the denominator, let's find a common denominator and subtract those:

Remember the trig identity that sin²(α) + cos²(α) = 1, so we know that 1 - cos²(α) = sin²(α). Plug this into the equation:

We now have [sin(α)/cos(α)] / [sin²(α)/cos(α)]. The cos(α) in the top and bottom cancel out, and we are left with sin(α) / sin²(α) = 1 / sin(α).

Remember that cosecant is the opposite of sine, so 1/sin(α) = csc(α).

~ an aesthetics lover

im here

step-by-step explanation: