`" if " f(0) = |{:(sin 0 ,,cos 0,,sin 0),(cos0,,sin0,,cos0),(cos0,, sin 0,,sin 0):}|` thenA. f(0)= 0 has exactly 2 real solutions in `[0 ,pi]`B. f(0) =0 has exactly 3 real solutions in `[0 ,pi]`C. range of function `(f(0))/(1-sin 2 0) " is " [-sqrt(2) , sqrt(2)]`D. range of fucntion .`(f(0))/(sin 2 0-1) " is " [-3,3]" is " [-3,3]`

`" if " f(0) = |{:(sin 0 ,,cos 0,,sin 0),(cos0,,sin0,,cos0),(cos0,, si

1.	`" if " f(0) = \|{:(sin 0 ,,cos 0,,sin 0),(cos0,,sin0,,cos0),(cos0,, sin 0,,sin 0):}\|` thenA. f(0)= 0 has exactly 2 real solutions in `[0 ,pi]`B. f(0) =0 has exactly 3 real solutions in `[0 ,pi]`C. range of function `(f(0))/(1-sin 2 0) " is " [-sqrt(2) , sqrt(2)]`D. range of fucntion .`(f(0))/(sin 2 0-1) " is " [-3,3]" is " [-3,3]`
Answer» Correct Answer - A::C `f(0) =sin^(3) 0 +cos^(3) 0 -cos 0 sin 0 (sin0 + cos 0)` `=(sin 0 + cos 0 )^(3) -4 sin 0 cos 0 (sin 0 + sin 0)` `=(sin 0 +cos 0) [1-sin 2 0]` `Now f(0)=0` `rArr tan 0 =-1 " or " sin 20 =1 ` `rArr f(0) =0` has 2 real solutions in `[0,pi]`