# CAT Practice : Trigonometry

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Number x lies between 0 and 1, higher powers of the number will be smaller than lower powers. Think about that. And then think about what does this have to do with Trigonometry.

## Range of function

Q.2: Sin2014x + Cos2014x = 1, x in the range of [-5π, 5π], how many values can x take?
1. 0
2. 10
3. 21
4. 11

Choice C. 21

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## Detailed Solution

We know that Sin2x + Cos2x = 1 for all values of x.
If Sin x or Cos x is equal to –1 or 1, then Sin2014x + Cos2014x will be equal to 1.

Sin x is equal to –1 or 1 when x = –4.5π or –3.5π or –2.5π or –1.5π or –0.5π or 0.5π or 1.5π or 2.5π or 3.5π or 4.5π.
Cosx is equal to –1 or 1 when x = –5π or –4π or –3π or –2π or –π or 0 or π or 2π or 3π or 4π or 5π.

For all other values of x, Sin2014 x will be strictly lesser than Sin2x.
For all other values of x, Cos2014 x will be strictly lesser than Cos2x.

We know that Sin2x + Cos2x is equal to 1. Hence, Sin2014x + Cos2014x will never be equal to 1 for all other values of x. Thus there are 21 values.

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