Question

If tan A= 5/6 , tan B = 1/11, prove that A+B=π/4
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Answer 1

Answer:

You have learned that a parallelogram is a closed, plane figure with four sides. It is a quadrilateral with two pairs of parallel, congruent sides. Its four interior angles add to 360° and any two adjacent angles are supplementary, meaning they add to 180° .

Step-by-step explanation:

(i) 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 proved.Read more on Sarthaks.com - https://www.sarthaks.com/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

Answer 2

Answer:

this answer

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 proved .