Please answer this trigonometry question correctly.

Please answer this trigonometry question correctly.

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1 Answers

Aditya Gupta
2081 Points
3 years ago
hello student, this is an extremely ez ques.
i am assuming the eqn is x^2 + 4 – 3cos(ax+b) – 2x= 0. write it as
(x – 1)^2 + 3= 3cos(ax+b)
here, max value of RHS is 3 whereas min value of LHS is 3 since (x – 1)^2 is always greater than equal to 0.
so for equality to hold, (x – 1)^2 must be equal to zero which means that x=1.
or 0+3= 3cos(a*1+b)= 3cos(a+b)
or cos(a+b)=1= cos0
this means that a+b= 0, 2pi, 4pi..... etc (as they cannot be less than zero).
but both a and b are also less than equal to 3. so the max value of a+b is 6, which is less than 2pi.
hence a+b can only be zero.
so, the final answer would be zero.
kindly approve :)

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