simplify please? (sin x) * (tan x + cot x)?

Answer 1

sinx * (sinx / cosx + cosx / sinx)
= sin^2 x / cosx + cos^2 x / cosx
= (sin^2 x + cos^2 x) / cosx
= 1 / cosx
= secx

Ask yo teacher if that correct, aight?

Answer 2

(sin x) * (tan x + cot x)
Need to know:
tan(x)=sin(x)/cos(x) and cot(x)=1/tan(x)
sin²(x)+cos²(x) = 1

Converting tan and cot into sin/cos and cos/sin
=[sin(x)][sin(x)/cos(x) +cos(x)/sin(x)]

Getting a common denominator i.e., sin(x) cos(x)
I put this on two lines because it gets truncated otherwise. Sorry
=[sin(x))[(sin²(x)+cos²(x))/
(sin(x)cos(x))

Since sin²(x)+cos²(x)=1,
=(sin(x)]{1/[(sin(x)cos(x)]}

= 1/cos(x) = sec(x)

Answer 3

= sin x( sinx/cosx+cos x/sin x) = sin x( sin^2+cos^2)/sin*cos=
1/cos x

Answer 4

(sin x) * (tan x + cot x) =
s(s/c + c/s) = s2/c + c =
(s2 + c2)/c = 1/cos(x) = secans(x)

Th

Answer 5

secx or 1/cosx