Question

Pls, answer this question ​

Answer 1

(Instead of θ, I use A)

Answer:

$\frac{1}{\sqrt{2}}$

Step-by-step explanation:

Given :

To find sin A if,

$tan A + cot A = 2$

Solution :

We know that,

$cotA = \frac{1}{tan A}$

So,

$tan A + cot A = 2$

⇒ $tanA +\frac{1}{tanA} = 2$

⇒ $\frac{tan^2A+1}{tanA} = 2$

⇒ $tan^2A + 1 = 2tanA$

⇒ $tan^2A - 2tanA + 1 = 0$

⇒ $tan^2A - tan A - tanA + 1 = 0$

⇒ $tanA(tanA - 1) - 1(tanA-1) = 0$

⇒ $(tanA - 1)(tanA - 1) = (tanA - 1)^2 = 0$

⇒ $tanA -1 = 0$

⇒ $tanA = 1$

⇒ A = 45°

Hence,

⇒ Sin A = Sin 45° = $\frac{1}{\sqrt{2}}$