Question

If sin????=a/b, find sec????+tan???? in terms of a and b.

Answer 1

Answer:

answer is thita I hope this helps you

Answer 2

secθ + tanθ = √(b+a)/(b-a)

Step-by-step explanation:

Given: sinθ = a / b

To find: secθ + tanθ in terms of a and b.

Solution:  

Sinθ = Opposite / Hypotenuse = a/b

Adjacent  =  √Hypotenuse² - Opposite² = √(b²- a²)

Cosθ = Adjacent / Hypotenuse =  √(b²- a²) / b

Now secθ + tanθ = 1/cosθ + Sinθ/Cosθ

  = (1 + Sinθ) / Cosθ

  = (1 + Sinθ) Cosθ/ Cos²θ  

  = (1 + Sinθ) Cosθ / 1 - Sin²θ

  = (1 + Sinθ) Cosθ / (1 + Sinθ) (1 - Sinθ)

  = Cosθ / 1 - Sinθ

  =   √(b²- a²) / b / 1-a/b

  =   √(b²- a²) / (b-a)

  =   [√(b + a)(b-a)] / (b-a)

  = √(b+a)/(b-a)

So secθ + tanθ = √(b+a)/(b-a)