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find the no. of solutions of the triplet (a,b,c) for which acos 2x+bcos²x+c=0 is satisfied for all values of x.

1 Answers

this expression is equal to

cos²x(2a+b) + c-a

This should be independent fo x...

so 2a+b=0

moreover this has to be equal to zero for all values of x.. so c-a=0

Hence a=-b/2=c

But this can be satisfied by infintiely many values of a, b, and c...

Hence infinite

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