Which of the following is TRUE ?AThe fundamental period of ∣ sin ⁡ x ∣ + ∣ cos ⁡ x ∣ BThe fundamental period of ∣ sin ⁡ x × cos ⁡ x ∣ CThe fundamental period of ∣ sin ⁡ x ∣ − ∣ cos ⁡ x ∣ DThe fundamental period of ∣ sin ⁡ x ∣

Question

Which of the following is TRUE ?AThe fundamental period of   ∣  sin  ⁡  x  ∣  +  ∣  cos  ⁡  x  ∣  BThe fundamental period of   ∣  sin  ⁡  x  ×  cos  ⁡  x  ∣  CThe fundamental period of   ∣  sin  ⁡  x  ∣  −  ∣  cos  ⁡  x  ∣  DThe fundamental period of   ∣  sin  ⁡  x  ∣

Lilia Nolan · Accepted Answer

The correct option is C    Let  f  (  x  )  =∣  sin  ⁡  x  ∣  +  ∣  cos  ⁡  x  ∣    f  (      π    2    +  x  )  =∣  −  sin  ⁡  x  ∣  +  ∣  cos  ⁡  x  ∣=∣  sin  ⁡  x  ∣  +  ∣  cos  ⁡  x  ∣=  f  (  x  )    Therefore, period is      π    2      Let  f  (  x  )  =∣  sin  ⁡  x  ∣  −  ∣  cos  ⁡  x  ∣    f  (      π    2    +  x  )  =∣  −  cos  ⁡  x  ∣  −  ∣  −  sin  ⁡  x  ∣=  −  f  (  x  )    f  (  π  +  x  )  =∣  sin  ⁡  x  ∣  −  ∣  −  cos  ⁡  x  ∣=  −  f  (  x  )    ⇒  Period is   π    Let  f  (  x  )  =∣  sin  ⁡  x  ×  cos  ⁡  x  ∣=      1    2    ∣  sin  ⁡  2  x  ∣