Question

How do you verify the identity `tan(pi/4-theta)=(1-tantheta)/(1+tantheta)`?

Answer 1

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"`