26 vote
If (sin A + cos A)/(sin A – cos A) = 5/4, the value of (tan2A + 1)/(tan2A - 1) = ?
If (sin A + cos A)/(sin A – cos A) = 5/4, the value of (tan2A + 1)/(tan2A - 1) = ?
1). 41/40
2). 12/13
3). 40/41
4). Not defined
1 answers
15 vote
(sin A + cos A)/(sin A – cos A) = 5/4
⇒ 4(sin A + cos A) = 5(sin A – cos A)
⇒ 9cosA = sinA(? sinx/cosx = tanx)
⇒ tanA = 9
We know that,
tan2x = 2tanx/(1 – tan2x)
⇒ tan2A = 2tanA/(1 – tan2A) = (2 × 9)/(1 – (9)2) = - 9/40
Then,
(tan2A + 1)/(tan2A - 1) = ( - 9/40 + 1)/( - 9/40 – 1) = - 31/49
As the above result is not given in the options, option d is correct.
