If , prove that

Given: Sin θ

We know that,

Or

Let,

Perpendicular =AB =m

and Hypotenuse =AC =√(m² + n²)

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

⇒ (m)² + (BC)² = (√(m² + n²))²

⇒ m² + (BC)² = m² + n²

⇒ (BC)² = m² + n² – m²

⇒ (BC)² = n²

⇒ BC =√n²

⇒ BC =±n

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

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

We know that,

Side adjacent to angle θ or base = BC =n

Hypotenuse = AC =√(m² + n²)

So,

Now, LHS = m sin θ +n cosθ

=√(m² + n²) = RHS

Hence Proved