Show that the following statement is true: tan(θ + π/4) - tan(θ - 3π/4) = 0Show complete solution and explain the answer

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to use the following formula such that:

`tan(theta + pi/4) = (tan theta + tan pi/4)/(1 - tan theta*tan (pi/4))`

Plugging `tan (pi/4) = 1`  in the formula above yields:

`tan(theta + pi/4) = (tan theta + 1)/(1 - tan theta)`

`tan(theta- (3pi)/4) = (tan theta- tan (3pi)/4)/(1+ tan theta*tan (3pi)/4)`

You should know that `tan (3pi/4) = tan (pi - pi/4) = -tan (pi/4)`

Hence `tan(theta +pi/4) = tan(theta- (3pi)/4)`

Writing the new form of expression yields:

`(tan theta + 1)/(1 - tan theta) - (tan theta + 1)/(1 - tan theta) = 0`

Hence, considering the identity `tan(theta +pi/4) = tan(theta- (3pi)/4)` , yields `tan(theta + pi/4)-tan(theta- (3pi)/4) = 0.`

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