Question -
Answer -
(i) If tan A = 5/6 and tan B = 1/11, prove that A + B =π/4
Given:
tan A = 5/6 and tan B = 1/11
We know that, tan (A + B) = (tan A + tan B) / (1 – tanA tan B)
= [(5/6) + (1/11)] / [1 – (5/6) × (1/11)]
= (55+6) / (66-5)
= 61/61
= 1
= tan 45o or tan π/4
So, tan (A + B) = tan π/4
∴ (A + B) = π/4
Hence proved.
(ii) If tan A = m/(m–1) and tan B = 1/(2m – 1), thenprove that A – B = π/4
Given:
tan A = m/(m–1) and tan B = 1/(2m – 1)
We know that, tan (A – B) = (tan A – tan B) / (1 + tanA tan B)
= (2m2 – m – m + 1) / (2m2 –m – 2m + 1 + m)
= (2m2 – 2m + 1) / (2m2 –2m + 1)
= 1
= tan 45o or tan π/4
So, tan (A – B) = tan π/4
∴ (A – B) = π/4
Hence proved.