Answer:
Step-by-step explanation:
sec(-x) − sin(-x) tan(-x)
So the first step is often to write everything in terms of sine, cosine, or tangent. So let's rewrite using sec x = 1 / cos x:
1/cos(-x) − sin(-x) tan(-x)
Now we need to deal with those -x angles. For that, we use reflection identities:
sin(-x) = -sin x
cos(-x) = cos x
tan(-x) = -tan x
Therefore:
1/cos(x) − sin(x) tan(x)
Now let's rewrite tan(x) as sin(x) / cos(x):
1/cos(x) − sin²(x)/cos(x)
Factoring:
(1 − sin²(x)) / cos(x)
Using Pythagorean identity: sin²(x) + cos²(x) = 1. So 1 − sin²(x) = cos²(x).
cos²(x) / cos(x)
And finally, we divide.
cos(x)
