Question

What is sinx/cosx + cosx/sinx

Answer 1

in order to add them, they need to have the same denominator

Answer 2

so what should the denominator be?

Answer 3

sin?

Answer 4

try again

Answer 5

Cos

Answer 6

the denominator should be a combination of cos and sin, because one fraction has sin, and the other has cos

so the GCF or LCD (i can never remember which) would be "sin(x)cos(x)"

Answer 7

Im confused... It would be: sinx/sinxcosx + cosx/sinxcosx?

Answer 8

slow down

you cant add them because the denominators are different,one is sin,and the other is cos

you need to change both the fractions so that they both have the denominator sinx cosx

Lets start by looking at the first fraction \[\frac{\sin x}{\cos{x}}\]in order to get teh denominator to become cos x sinx, we need to multiply a sin x to the denominator,

but you can't just multiply 1/ sin x, otherwise you would get a completely different fraction

the solution would be to multiply 1 because 1 times any number will be the number
\[1=\frac{\sin x}{\sin x}\]
\[\frac{\sin x}{\cos{x}}*1=\frac{\sin x}{\cos{x}}*\frac{\sin x}{\sin x}= \frac{{\sin}^2 x}{\sin x \cos x}\]


now we need to do the same process for the other fraction

Answer 9

so what do you think the other fraction will look like?

Answer 10

cos^2/sinxcosx

Answer 11

right, good job

now since they both have the same denominator, you can add up the numerators

\[\frac{\sin^2 x}{\sin x \cos x} + \frac{\cos^2 x}{\sin x \cos x}\]

\[\frac{\cos^2 x+\sin^2 x}{\sin x \cos x}\]

Answer 12

also know the trig identity

\[\sin^2 x+\cos^2 x =1\]