Question

b sin β=a sin(2α+β)prove that (b+a)cot(α+β)=(b-a) cotα.​

Answer 1

Answer:

Step-by-step explanation:

 bsin β =  asin(2α+β)

asin2αcosβ + acos2αsinβ = bsinβ

a/bsin2αcotβ + a/bcos2α = 1

asin2αcotβ + acos2α = b

asin2αcotβ = (b - acos2α)

cotβ  =  (b - acos2α)/asin2α

tanβ = asin2α/ (b - acos2α)

LHS = (b+a)cot(α+β) =  (b+a)/tan (α+β) =  (b+a)(1-tanαtanβ )/(tnα +tanβ )