Answer:
sec(x)
Step-by-step explanation:
tan x * sinx + cos x
Tan x = sin x/ cos x
Replace tan x in the equation
sinx /cosx * sin x + cos x
sin^2 x / cos x + cos x
We know sin^2 x = 1 -cos^2 x
Replace sin^2 with 1 -cos ^2 x
(1 -cos^2 x) / cos x + cos
Distribute the denominator
1 /cos x - cos x + cos x
Combine like terms
1/cos x
sec x
