Question

23
If cos2B = cos(A+C)
then-
cos(A-C)
(A) tanA, tanB, tanc are in A.P.
(B) tanA, tanB, tanC are in G.P.
(C) tanA, tanB, tanC are in H.P.
(D) None of these
(A) tama, tanb
tanc are Gp​

Answer 1

Answer:

cos(A-C)

your mean ?

Answer 2

Answer:

$\sf Answer࿐$

Explanation:

cos2B=cos(A−C)cos(A+C)

Using componendo-dividendo

cos2B−1cos2B+1=cos(A+C)−cos(A−C)cos(A+C)+cos(A−C)

1−2sin2B−12cos2B−1+1=cosAcosC−

sinAsinC−cosAcosC−sinAsinCcosAcosC−sin

AsinC+cosAcosC+sinAsinC

−cot2B=−cotAcotC

tan2B=tanAtanC

Hence tanA,tanB,tanC are in G.P