If , find the value of tan²θ + sinθ cosθ + cotθ.

Given: Sin θ

We know that,

Or

Let,

Perpendicular =AB =3k

and Hypotenuse =AC =5k

where, k is any positive integer

So, by Pythagoras theorem, we can find the third side of a triangle

In right angled ∆ ABC, we have

⇒ (AB)² + (BC)² = (AC)²

⇒ (3k)² + (BC)² = (5k)²

⇒ 9k² + (BC)² = 25k²

⇒ (BC)² = 25 k² –9k²

⇒ (BC)² = 16k²

⇒ BC =√16k²

⇒ BC =±4k

But side BC can’t be negative. So, BC = 4k

Now, we have to find the value of cos θ and tan θ

We know that,

The side adjacent to angle θ or base = BC =4k

Hypotenuse = AC =5k

So,

Now,

We know that,

Perpendicular = AB =3k

Base = BC =4k

So,

Now, tan² θ + sin θ cos θ + cot θ