Question

let (tan3A/tanA)=K,where tan A not equal to 0 and K not equal to 1/3.
what is tan^2 A equal to?​

Answer 1

Answer:

tan3A/tanA = k

sin3AcosA/cos3AsinA = k

using componendo and dividendo

(sin3AcosA + cos3AsinA). k + 1

------------------------------------- = ---------

sin3AcosA - cos3AsinA. k - 1

sin(3A+A)/sin(3A-A). = (k+1)/(k-1)

sin4A/sin2A = (k+1)/(k-1)

2sin2Acos2A/sin2A = (k+1)/(k-1)

cos2A = (k+1)/2(k-1)

((1-tan^2A)/(1+tan^2A) = (k+1)/(2k-2)

using componendo and dividendo again

(1+tan^2A)-(1-tan^2A)/(1+tan^2A)+(1-tan^2A) = (2k-2)-(k+1)/(2k-2)+(k+1)

2tan^2A/2 = (k-3)/(3k-1)

tan^2A = (k-3)/(3k-1)

Answer 2

Answer:

Step-by-step explanation: