Question

tan A = 5/6 , tan B = 1/11

then (A+B) = Pi radian/2
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Answer 1

Step-by-step explanation:

Given as tan A = 5/6 and tan B = 1/11 As we know that, tan (A + B) = (tan A + tan B)/(1 – tan A tan B) = [(5/6) + (1/11)]/[1 – (5/6) × (1/11)] = (55 + 6) / (66 - 5) = 61/61 = 1 = tan 45o or tan π/4 Therefore, tan (A + B) = tan π/4 ∴ (A + B) = π/4 Thus proved. (ii) Given as tan A = m/(m – 1) and tan B = 1/(2m – 1) As we know that, tan (A – B) = (tan A – tan B)/(1 + tan A tan B) = (2m2 – m – m + 1)/(2m2 – m – 2m + 1 + m) = (2m2 – 2m + 1)/(2m2 – 2m + 1) = 1 = tan 45o or tan π/4 Therefore, tan (A – B) = tan π/4 ∴ (A – B) = π/4 Thus prove 654642/i-if-tan-a-5-6-and-tan-b-1-11-prove-that-a-b-4-ii-if-tan-a-m-m-1-and-tan-b-1-2m-1-then-prove-that-a-b-4