How do you verify the identity #tan(pi/4-theta)=(1-tantheta)/(1+tantheta)#?
1 Answer
Feb 10, 2017
see explanation.
Explanation:
Using the
#color(blue)"addition formula for tangent"#
#color(red)(bar(ul(|color(white)(2/2)color(black)(tan(a±b)=(tana±tanb)/(1∓tanatanb))color(white)(2/2)|)))# There are 3 approaches to verifying an identity.
#• " manipulate left side into the form of the right side"#
#• " manipulate right side into the form of the left side"#
#• " manipulate both sides until a common point is reached"# Using the first approach.
#" left side "=tan(pi/4-theta)# Expand using the above addition formula for
#tan(a-b)#
#rArr(tan(pi/4)-tantheta)/(1+tan(pi/4)tantheta)#
#color(orange)"Reminder " tan(pi/4)=1#
#rArr(1-tantheta)/(1+tantheta)=" right side"to" verified"#