If 5 tan α = 4, show that .

Given: 5 tan = 4

⇒ tan α

We know that,

Or

Let,

The side opposite to angle α =AB = 4k

The side adjacent to angle α =BC = 5k

where k is any positive integer

Firstly we have to find the value of AC.

So, we can find the value of AC with the help of Pythagoras theorem

⇒ (AB)² + (BC)² = (AC)²

⇒ (4k)² + (5k)² = (AC)²

⇒ (AC)² = 16k²+25k²

⇒ (AC)² = 41k²

⇒ AC =√41k²

⇒ AC =±k√41

But side AC can’t be negative. So, AC = k√41

Now, we will find the sin α and cos α

We know that

Side adjacent to angle α = BC = 5k

and Hypotenuse = AC = k√41

So,

And

Side adjacent to angle α =AB = 4k

And Hypotenuse =AC = k√5

So,

Now, LHS

= RHS

Hence Proved