How do you verify the identity: #tan (x + pi/2) = -cot x#?
2 Answers
Jun 9, 2015
Verify tan (x + pi/2) = - cot x
Explanation:
On the trig unit circle, the value AT = tan x rotates counterclockwise an arc of pi/2, and becomes BU = - cot x
Jun 24, 2016
Note that
For the numerator, use
#sin(x+pi/2)=sin(x)cos(pi/2)+cos(x)sin(pi/2)#
#=sin(x)*0+cos(x)*1#
#=cos(x)#
In the denominator, use
#cos(x+pi/2)=cos(x)cos(pi/2)-sin(x)sin(pi/2)#
#=cos(x)*0-sin(x)*1#
#=-sin(x)#
Thus, we see that
#tan(x+pi/2)=sin(x+pi/2)/cos(x+pi/2)=cos(x)/(-sin(x))=-cot(x)#
#square#