If 0 < θ < 90°, 3b cosec θ = a sec θ and 3a sec θ - b cosec θ = 8, then the value of $9b^2 + a^2$ is :
Answer & explanation
Correct answer: option 3
Given :-
3b cosec θ = a sec θ -----(1)
and 3a sec θ - b cosec θ = 8 -----(2)
multiply equation 1 by 3 .
9b cosec θ = 3a sec θ
By putting value of ( 3a sec θ ) into equation 2.
9b cosec θ - b cosec θ = 8
8b cosec θ = 8
b cosec θ = 1
b = sinθ
Put value of ' b ' into equation 1.
3b cosec θ = a sec θ
3 × sinθ . cosec θ = a sec θ
a = 3 cosθ
Now,
9b² + a²
= 9 ( sin²θ ) + (3 cosθ)²
= 9 ( sin²θ + cos²θ )
= 9 { sin²θ + cos²θ = 1 }