Q. 26 A

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

Answer :

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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