Posted by lindsay on Tuesday, May 1, 2012 at 4:35pm.
Given that tan A = 2 tan B (B is the symbol for Beta) show that tan (AB) = sin 2B/3 cos2 Beta.

trigonometry  Reiny, Tuesday, May 1, 2012 at 4:52pm
tan(AB) = (tanA  tanB)/(1+tanAtanB)
but tanA = 2tanB
so above
= (2tanB  tanB)/(1 + 2tanBtanB)
= tanB/(1+2tan^2B)
= (sinB/cosB) / (1 + 2sin^2 B /cos^2 B)
= sinB/cosB /[(cos^2 B + 2sin^2 B)/cos^2 B]
= (sinB/cosB) * (cos^2 B)/(cos^2 B + 2sin^2 B)
= sinBcosB /(cos^2 B + 2(1  cos^2 B) )
= sinBcosB / (2  cos^2 B)
= 2sinBcosB/ (4  2cos^2 B)
= sin 2B / (4  2cos^2 B)
which is different from yours,
I can't seem to find my error if there is one.
Answer This Question
Related Questions
 Trigonometry  Find the exact value of tan(ab) sin a = 4/5, 3pi/2<a<pi...
 trig  evaluate the following in exact form, where the angeles alpha and beta ...
 Calculus  The question will first read in English followed by a reading in ...
 Trigonometry  Prove that tan (Beta) sin (Beta) + cos (Beta) = sec (Beta) Please...
 physics  Two radar stations A and B, are separated by horizontal distance of (a...
 Math  Given that sin alpha=4/sqrt65, pi/2<alpha<pi, and cos beta=3/...
 Trig  Use the fundamental identities to simplify the expression: cot beta sec ...
 Trigonometry  5. Prove: Tan beta sin beta + cos beta = sec beta 6. Prove: ( tan...
 Trigonometry  5. Prove: Tan beta sin beta + cos beta = sec beta 6. Prove: ( tan...
 pre calc  suppose beta is an angle in the second quadrant and tan beta=2. Fine...
More Related Questions