Answer :

It is given that 3 cot A = 4

Consider a right triangle ABC, right-angled at point B

To Find : Cos^{2}A – Sin^{2}A or not

Cot A =

=

This fraction shows that if the length of base will be 4 then the altitude will be 3. And base and altitude will both increase with this propotion only. Let AB be 4k then BC will be 3k

In ΔABC,

Pythagoras theorem : It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

By pythagoras theorem

(AC)^{2} = (AB)^{2} + (BC)^{2}

= (4*k*)^{2} + (3*k*)^{2}

= 16*k*^{2} + 9*k*^{2}

= 25*k*^{2}

AC = 5*k*

Cos A =

=

=

And also we know that,

Sin A =

=

=

And ,Tan A =

=

=

Now putting the values so obtained we get,

= 7/25

Cos^{2}A – Sin^{2}A =

=

=

Therefore,

Cos^{2}A – Sin^{2}A

Hence, the expression is correct.

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