Question

Trig question please save mee simplify each expression to one trig function or number

Answer 1

sec x

Explanation:

tan x * sin x + cos x = (sin x/cos x)sin x + cos x = sin^2 cos x + cos x = (1-cos^2x)/cos x + cos x = 1/cos x - cos x+ cos x = 1/cos x = sec x

Answer 2

sec(x)

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