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NTA Abhyas JEE Main2020MathematicsFunctionsPractice

sin a x + cos a x and | sin x | + | cos x | are periodic with the same fundamental period, if a equals to

Options

  1. A0
  2. B1
  3. C2
  4. D4

Correct answer

D. 4

Step-by-step solution

s i n a x + cos a x = 2 sin a x + π 4 So, fundamental period = 2 π a Let, T be the fundamental period of sin x + cos x So sin ( x + T ) + cos ( x + T ) =   sin x + cos x . Squaring both sides, we get, 1 + s i n ( 2 x + 2 T ) = 1 + sin 2 x Therefore, the fundamental period of s i n x + c o s x is π 2 Hence, 2 π a = π 2 ⇒ a = 4

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