If sin , then find the value of cos θ and tan θ.

Given: Sin θ

We know that,

Or

Let,

Side opposite to angle θ = 12k

and Hypotenuse = 13k

where, k is any positive integer

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

⇒ (AB)² + (BC)² = (AC)²

⇒ (12k)² + (BCk)² = (13)²

⇒ 144 k² + (BC)² = 169 k²

⇒ (BC)² = 169 k² –144 k²

⇒ (BC)² = 25 k²

⇒ BC =√25 k²

⇒ BC =±5k

But side BC can’t be negative. So, BC = 5k

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

We know that,

Side adjacent to angle θ = BC =5k

Hypotenuse = AC =13k

So,

Now, tan θ

We know that,

side opposite to angle θ = AB =12k

Side adjacent to angle θ = BC =5k

So,