Question

if sec theta + tan theta = 2. find sin theta { theta belongs to(0-90°)}​

Answer 1

Answer:3/5

Step-by-step explanation:secθ+tanθ=2⟶(1)

Now, sec^2θ−tan^2θ=1

⇒(secθ−tanθ)(secθ+tanθ)=1

⇒2(secθ−tanθ)=1

⇒secθ−tanθ=1/2 ⟶(2)

Adding equations (1)&(2), we get

⇒2secθ=2+1/2 =5/2

⇒secθ=5/4

Or cosθ=4/5

Now, sinθ=$\sqrt{1-cos^2$∅

$\sqrt{1-(4/5)^2} \\\sqrt{1-16/25\\} \\\sqrt{9//25}$

Hence,the answer is 3/5