# 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 =±k41

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

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