## anonymous one year ago Verify the identity. cot (x-pi/2)= -tan x

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1. anonymous

Working on the left hand side, you get: $\frac{ 1 }{ \tan (x-\frac{ \Pi }{ 2 }) }$ After that, follow the property that:$\tan(A-B)=\frac{ tanA-tanB }{ 1+tanAtanB }$ Giving us: $\frac{ 1 }{ \frac{ tanx-\tan \frac{ \Pi }{ 2 } }{ 1+tanxtan \frac{ \Pi }{ 2 } } }=\frac{ 1+tanxtan \frac{ \Pi }{ 2 } }{ tanx-\tan \frac{ \Pi }{ 2 } }$

2. anonymous

From here, we can use the calculator to find tan pi/2 .

3. hartnn

or you could convert cot into cos/sin and directly use, cos (x-pi/2) = sin x sin (x-pi/2) = -cos x