Sin alpha /sin beta=root3/2
Cos alpha/cos beta=root5/2
Find the value of 2tan square beta+ tan square alpha=?
Answers
Given : Sinα / Sinβ = √3 / 2 , Cosα / Cosβ = √5 / 2
To Find : Value of 2 tan²β + tan²α
Solution:
Sinα / Sinβ = √3 / 2
=> Sinα = √3 Sinβ / 2
=> Sin²α = 3 Sin²β /4
Cosα / Cosβ = √5 / 2
=> Cosα = √5 Cosβ / 2
=> Cos²α = 5 Cos²β /4
Squaring both sides and add
=> Sin²α + Cos²α = 3 Sin²β /4 + 5 Cos²β /4
=> 1 = (3/4)(Sin²β +Cos²β) + (2/4)Cos²β
=> 1 = 3/4 + (1/2)Cos²β
=> 1/4 = (1/2)Cos²β
=> Cos²β = 1/2
=> Sin²β = 1 - Cos²β = 1 -1/2 = 1/2
Sin²β/Cos²β = (1/2) /(1/2)
=> tan²β = 1
Sin²α = 3 Sin²β /4
Cos²α = 5 Cos²β /4
=> (Sin²α/ Cos²α ) = (3 Sin²β /4)/ (5 Cos²β /4)
=> tan²α = (3/5) tan²β
=> tan²α = 3/5
2 tan²β + tan²α
= 2(1) + 3/5
= 2 + 3/5
= 13/5
= 2.6
2 tan²β + tan²α = 2.6
Learn More:
Prove that sinα + sinβ + sinγ − sin(α + β+ γ)
https://brainly.in/question/10480120
[tex]left[egin{array}{ccc}0&tan(alpha/2)\tan(alpha/2)&0 ...
https://brainly.in/question/17326856