Question

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

Answer 1

Hope it is helpful
Mark brainliest if it was correct

Answer 2

Answer:

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°