Question

sina/sinb=root 2 and tana/tabb=root 3.find a and b

Answer 1

sinA/sinB=√2
tanA/tanB=√ 3

⇒tanA/tanB=√3

⇒sinA/cosA/sinB/cosB=√ 3
⇒sinA cosB/cosA sinB=√3

Put the value of sinA/sinB

⇒√2cosB/cosA=√3

⇒cosB/cosA=√3/√2

⇒√(1−sin^2B)/√(1−sin^2A) =√3/√2

⇒√(1−sin^2^B)/√(1−2sin^2√B)=√3/√2

⇒2(1−sin^2B) = 3(1−2sin^2B)
⇒
2−2sin^2B=3−6sin^2B

⇒4sin^2B=1
⇒sin^2B=1/4
⇒sinB= ±1/2 For acute angles
sinB= sin30°
⇒
B=30°
sinA=sinB√2

⇒sinA=2/√2
Multiply √2 we can get

⇒sinA= 1 /√2
⇒A=45°
Thus,A=45° and B=30°
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