Question

if sec theta +tan theta=5/3 then, sin theta​

Answer 1

Answer:

Value of sinθ = 8/17

Step-by-step explanation:

secθ + tanθ = 5/3 ---------(1)

=>(secθ + tanθ)(secθ - tanθ) =5/3 (secθ - tanθ)

=> sec²θ - tan²θ =5/3 (secθ - tanθ)

=> 1 = 5/3 (secθ - tanθ)

=> secθ - tanθ = 3/5 ----------(2)

From (1)+(2) , we get, 2secθ = 34/15 => secθ = 17/15 => cosθ =15/17

Now, sin²θ = 1-cos²θ => sin²θ = 1- 225/289 =64/289 => sinθ = 8/17