Here is a slightly tough question in CAT 2019. It combines the topics of trigonometry and algebra. It is very important to have done a solid **CAT Preparation** to be sure about the concepts and trigonometry formula to even attempt this question. Once you are clear with the concepts & formulas, it would be prudent to practice them from **CAT previous year paper**.

Question 17 : The number of the real roots of the equation 2cos(x(x + 1)) = 2^{x} + 2^{-x} is

- 0
- Infinite
- 1
- 2

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2cos (x(x + 1)) = 2^{x} + 2^{-x}

Consider RHS, 2^{x} + 2^{-x}

This is of the form,

We know that when y is positive and when y is negative

Here, since we are dealing with 2^{x}, is considered

So, 2cos (x (x + 1))

Substitute x = 0, 2^{x} + 2^{-x }= 2^{0} + 2^{0 }= 2

2cos (x (x + 1)) = 2cos (0(0 + 1)) = 2cos (0) = 2 x = 0 is a valid solution

Any value other than this wont work.

Therefore, only x = 0 works and there is only one real solution

The question is **"The number of the real roots of the equation 2cos(x(x + 1)) = 2 ^{x} + 2^{-x} is " **

**Choice C** is the correct answer.

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