How do you verify the identity $\frac{cos (\frac{π}{2} - x)}{sin (\frac{π}{2} - x)} = tan x$ $cos(pi/2-x)/sin(pi/2-x)=tanx$ ?

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Answer 1 · 2017-02-06T05:48:11

Since

$cos (\frac{π}{2} - α) = sin α$ $cos(pi/2-alpha)=sinalpha$

and

$sin (\frac{π}{2} - α) = cos α$ $sin(pi/2-alpha)=cosalpha$ ,

you get:

$\frac{cos (\frac{π}{2} - x)}{sin (\frac{π}{2} - x)} = \frac{sin x}{cos x} = tan x$ $cos(pi/2-x)/sin(pi/2-x)=sinx/cosx=tanx$

How do you verify the identity cos(pi/2-x)/sin(pi/2-x)=tanxcos(π2−x)sin(π2−x)=tanxcos(pi/2-x)/sin(pi/2-x)=tanx?