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if 2CosA = x+ 1/x and 2CosB = y+ 1/y then find 2cos(A+B) (A) x/y +y/x (B) x/y-y/x (C) 2y/x (D) 2x/y

 
if 2CosA = x+ 1/x and 2CosB = y+ 1/y then find 2cos(A+B)
(A) x/y +y/x
(B) x/y-y/x
(C) 2y/x
(D) 2x/y

Grade:

1 Answers

Kaustubh Nayyar
27 Points
7 years ago
For any real ‘a’ and ‘1/a’ AM > GM ( arithmetic mean greater than or equal to                                                                                           geometric mean)
hence a + 1/a > 2 ( a . 1/a )1/2     whic gives a + 1/a > 2
hence x + 1/x and y + 1/y both are > 2
But cos function lies between  – 1 and 1 which gives twice cos function lies between – 2 and 2
in both cases ( of x and y)   LHS  2  and RHS > 2  But both are equal to each other hence LHS = RHS = 2 
this gives cosA = cos B = 1     →   A = B = 0 
hence 2cos(A + B ) = 2

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