Q. 43 A4.3( 4 Votes )

If , prove that : 3 cos B – 4cos3 B = 0

Answer :

Given:


We know that,



Or



Let,


Perpendicular =AB =k


and Hypotenuse =AC =2k


where, k is any positive integer


So, by Pythagoras theorem, we can find the third side of a triangle


In right angled ABC, we have


(AB)2 + (BC)2 = (AC)2


(k)2 + (BC)2 = (2k)2


k2 + (BC)2 = 4k2


(BC)2 = 4k2 –k2


(BC)2 = 3k2


BC =3k2


BC =k3


So, BC = k√3


Now, we have to find the value of cos B


We know that,



Side adjacent to angle B or base = BC = k√3


Hypotenuse = AC =2k


So,


Now, LHS = 3 cos B – 4cos3 B





=RHS


Hence Proved


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