If 3 cot A = 4, check whether =cos²A–sin² A or not.

Given: 3cot A = 4

We know that,

Or

Let,

Side adjacent to angle A =AB = 4k

The side opposite to angle A =BC = 3k

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 + (3k)² = (AC)²

⇒ (AC)² = 16 k² + 9 k²

⇒ (AC)² = 25 k²

⇒ AC =√25k²

⇒ AC = ±5k [taking positive square root since, side cannot be negative]

and

Now,

…(i)

And RHS = cos² A – sin² A

=

…(ii)

From Eqs. (i) and (ii) LHS =RHS

Hence Proved