Question

sec theta + tan theta=2. find value of sin theta.​

Answer 1

We know that

sec²θ - tan²θ = 1

sin²θ + tan²θ = 1

By using a² - b² =(a+b) (a-b)

(secθ + tanθ) (secθ + tanθ) = 1

then ,

Given that secθ - tanθ = 2

2(secθ + tanθ)= 1

secθ + tanθ = 1/2

By eliminating we get :

secθ - tanθ = 2

secθ + tanθ = 1/2

(secθ - tanθ) (secθ + tanθ) =2 + 1/2

2secθ = 5/2

secθ = 5/4

cosθ = 4/5

By using first identity

sin²θ + (4/5) ² =1

sin²θ + 16/25 = 1

sin²θ = 9/25

sinθ = ±3/5

Let's check which quadrant that sinθ fall to:

secθ = 5/4(+)

secθ + tanθ = 2

5/4 + tanθ = 2

θ = 3/4(+)

That means sinθ falls in first quadrant , meaning

sinθ = 3/5