SOLUTION: Please verify by changing the left side only: tan(pi/4-x) = (cosx-sinx)/(cosx+sinx)

Question 672324: Please verify by changing the left side only:
tan(pi/4-x) = (cosx-sinx)/(cosx+sinx)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Please verify by changing the left side only:
tan(pi/4-x) = (cosx-sinx)/(cosx+sinx)
**
Identity: tan(s-t)=(tan s-tan t)/(1+tan s tan t)
tan(π/4-x)=(tan π/4-tan x)/(1+tan π/4 tan x)
tan π/4=1
=(1-tan x)/(1+tan x)
=[1-(sin x/cos x)]/[1+(sin x/cos x)]
=[(cos x-sin x)/cos x)]/[(cos x+sin x)/cos x)]
cos x in denominator cancels out
=(cos x-sin x)/(cos x+sin x)
verified: left side=right side
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