Q. 204.0( 3 Votes )

If , then find the values of cos θ and .

Answer :



We know that,



Or,



Let,


Side opposite to angle θ = AB = x2 – y2


and Hypotenuse = AC = x2 + y2


In right angled ∆ABC, we have


(AB)2 + (BC)2 = (AC)2 [by using Pythagoras theorem]


(x2 – y2 )2 + (BC)2 = (x2 + y2 )2


(BC)2 = (x2 + y2 )2 – (x2 – y2 )2


Using the identity, a2 – b2 = (a+b)(a – b)


(BC)2 = [(x2 + y2 + x2 – y2 )][ x2 + y2 –( x2 – y2)]


(BC)2 = (2x2)(2y2)


(BC)2 = (4x2y2)


BC =√4x2y2


BC = ±2xy


BC = 2xy [taking positive square root since, side cannot be negative]



and


So,


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