tan(x)/sec(x)=?

Question

A. 1/sin(x)
B. sin(x)
C. cos(x)/sin^2(x)
D.sin(x)/cos^2(x)

Answer 1

Actually this is a trick question.

tan(x)/sec(x) = sin(x) but with the restriction that {x|x is not k Pi/2 where k is an integer} because both sec(x) and tan(x) are not defined for Pi/2, 3PI/2, 5PI/2, etc but sin is defined at these points.

The true answer is without the restriction, NONE of the answers are truly correct.

If you teacher argues differently,
say f(x) = sin(x) what is f(pi/2) = sin(pi/2) = 1
f(x) = tan(pi/2)/sec(pi/2) what is f(pi/2) = tan(pi/2)/sec(pi/2) = undefined.

Two different answers!

Likewise
f(x) = sin(x) then f(3pi/2) = -1
f(x) = tan(x)/sec(x) then f(3pi/2) = tan(3pi/2)/sec(3pi/2) = undefined.

so they have different domains and unless x is restricted in the question, the right answer is none of the above.

Answer 2

ok lets start by : tan x = sinx / cosx , sec x = 1/ cos x
so we are going to divide tan by sec
sinx/cosx divided 1/cosx
sinx / cosx times cosx = sinx so answer no. b is correct
i hope that helps

Answer 3

B
(sinx/cosx) / (1/cosX)= sin x

Answer 4

tan x/sec x = sinx/cosx *cosx= sinx (B)

Answer 5

tanx/secx
= tanx/1/cosx
=opp/adj/hyp/adj
=opp/hyp
= sin x

b