Question

Cos( - x) + tan( – x)sin( – x)

Answer 1

sec x

Explanation:

cos (-x) = cos x (even function)

tan (-x) = -tan x = -sin x / cos x

sin (-x) = - sin x (odd function)

Then: cos( - x) + tan( – x)sin( – x) becomes:

sin x -sin x

cos(x) - ------------ * -----------

cos x 1

or

cos²x sin²x 1

------------ + ------------ = --------------- = sec x (answer)

cos x 1 cos x

Answer 2

sec x.

Explanation:

cos( - x) + tan( – x)sin( – x)

= cos(-x) + sin(-x)sin(-x) / cos(-x)

= cos(-x)(cos(-x) + sin^2x / cos(-x)

= (cos^2x + sin^2 x) / cos(-x)

= 1 / cos(-x)

= 1 /cos x

= sec x.

= sec (-x).