cos^[(pi/2)-x]/ cos x

Match the trig expression with one of the following
a) csc x
b) tan x
c) sin^2 x
d) sin x tan x
e) sec^2 x
f)sec^2 x + tan^2 x

Question

cos^[(pi/2)-x]/ cos x

Match the trig expression with one of the following
a) csc x
b) tan x
c) sin^2 x
d) sin x tan x
e) sec^2 x
f)sec^2 x + tan^2 x

anonymous · Answer

cos^[(pi/2)-x]/ cos x = sin x/ cos x = tan x
Hence option b is correct

anonymous · Answer

cos^2[(pi/2)-x]/cos x
there was a typo
is the answer still the same?

jdoe0001 · Answer

well, the answer will still hold, with just an extra sine function
so 
$$
\cfrac{cos^2\pmatrix{\frac{\pi}{2}-x}}{cos(x)}\
\implies \cfrac{sin^2(x)}{cos(x)} \implies sin(x)\cfrac{sin(x)}{cos(x)} \implies sin(x)tan(x)
$$

anonymous · Answer

@jdoe0001 could you explain how you got the first part?

jdoe0001 · Answer

http://1.bp.blogspot.com/-57vrQkzCnVA/TxfkOuTBs6I/AAAAAAAABWU/R91jwBewUyE/s1600/cofunction+identities.png cofunction identities