Q. 26 A

# 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

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