UPSEE Solved Model Paper 6

We can solve this problem using the trigonometric function of sum and difference
compound angles :
An algebraic sum of two or more angles is called a compound angle
tan (A + B) =

tanA+tanB

1−tanAtanB

By using this formula we can find the calue of tan 3A - tan 2A - tan A
We have
tan 3A - tan 2A - tan A
Write , tan 3A as tan (2a + A)
tan 3A = tan (2A + A)
tan 3A =

tan2A+tanA

1−tan2AtanA

Since tan (A + B) =

tan2A+tanA

1−tanAtanB

tan 3A (1 - tan 2A tan A) = tan 2A + tan A
tan 3A - tan 3A tan 2A tan A = tan 2A + tan A
tan 3A - tan 2A - tan A = tan 3A . tan 2A . tan A
Therefore
tan 3A - tan 2A - tan A = tan 3A . tan 2A . tan A