The question is from CAT Geometry - Trigonometry. This is about trigonometric functions. We need to find out the number of possible values x can take. Trigonometry is an important topic for CAT Preparation for the CAT Exam. Trigonometric ideas can be completely opposite, as in, some questions test lot of common sense with direction, heights and distances, while others could test you on identities. CAT exam could test one on both these fronts. Make sure you master both in CAT - Trigonometry.
Question 2: Sin2014x + Cos2014x = 1, x in the range of [-5π, 5π], how many values can x take?
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.
The question is "How many values the 'x' can take?"
Choice C is the correct answer.
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