question_answer

If\[co{{s}^{-1}}\left( cosx \right)=\sqrt{1+sin2x}\forall \,x\in (0,2\pi )\], then no. of solution =

A) 2                     

B)        4     

C) 3                     

D)        5

Correct Answer: A

Solution :

[a] \[\sqrt{1+sin2x}=\left| sinx+cosx \right|\] \[=\sqrt{2}=\left| sin\left( x+\frac{\pi }{4} \right) \right|\]