Question

5 tan square theta + 3 = 9 sec theta

Answer 1

θ = 60°

Step-by-step explanation:

Find the acute angle theta such that 5tan square theta + 3 = 9 sec theta

5Tan²θ + 3 = 9Secθ

Using

Sec²θ = Tan²θ + 1

=> Tan²θ = Sec²θ - 1

5(Sec²θ - 1) + 3 = 9 Secθ

=> 5Sec²θ - 9Secθ - 2 = 0

=> 5Sec²θ - 10Secθ + Secθ - 2 = 0

=> 5Secθ(Secθ - 2) + 1(Secθ - 2) = 0

=> (5Secθ + 1)(Secθ - 2) = 0

Secθ = -1/5 => Cosθ = -5 (not possible)

Secθ = 2 => Cosθ = 1/2 => θ = 60°

Answer 2

Using, sec²x - tan²x =1

theta=60°