Question
Prove:
1-tanx/1+tanx=1-sin2x/cos2x
1-tanx/1+tanx=1-sin2x/cos2x
Answers
Steve
multiply by 1-tanx to get
(1-tanx)^2/(1-tan^2 x)
= (1-2tanx+tan^2 x)/(1-tan^2 x)
= (1+tan^2 x)/(1-tan^2 x) - 2tanx/(1-tan^2 x)
= sec^2x/(1-tan^2 x) - tan2x
= 1/(cos^2x-sin^2x) - tan2x
= 1/cos2x - sin2x/cos2x
= (1-sin2x)/cos2x
Your carelessness with parentheses threw me off for a while. I was reading the RS as 1-(sin2x/cos2x) using the normal order of operations.
(1-tanx)^2/(1-tan^2 x)
= (1-2tanx+tan^2 x)/(1-tan^2 x)
= (1+tan^2 x)/(1-tan^2 x) - 2tanx/(1-tan^2 x)
= sec^2x/(1-tan^2 x) - tan2x
= 1/(cos^2x-sin^2x) - tan2x
= 1/cos2x - sin2x/cos2x
= (1-sin2x)/cos2x
Your carelessness with parentheses threw me off for a while. I was reading the RS as 1-(sin2x/cos2x) using the normal order of operations.
Xiumin
lol im sorry. Thanks Steve! :)