complete the identity

Question

sin x/ cos x + cos x/ sin x = ?

Answer 1

sin x / cos x + cos x / sin x

To combine any fractions, you create a common denominator. You can do it like this:

sin x / cos x • sin x / sin x + cos x / sin x • cos x / cos x

and get:

(sin²x + cos²x) / (cos x sin x) ( BTW sin²x is the standard way of writing (sin x)².)

And a really cool thing about trigonometry is the Pythagorean identity: sin²x + cos²x = 1

So this becomes:

1 / (cos x sin x)

I think this is what your teacher is looking for.

Answer 2

Hi Ds D,

Simplify is a better term than complete.

sin(x)/cos(x) + cos(x)/sin(x)

Adding the two fractions together:

(sin²(x) + cos²(x))/(cos(x)sin(x))

Because of a pythagorean identity:

1/(cos(x)sin(x))

because of reciprocal identities:

sec(x)csc(x)

You are a Math Person