If  −π/4≤x≤π/4,then the  number of distinct real roots of sin⁡xcos⁡xcos⁡xcos⁡xsin⁡xcos⁡xcos⁡xcos⁡xsin⁡x=0  is

Using C1→C1+C2+C3,Δ=sin⁡x+2cos⁡xcos⁡xcos⁡xsin⁡x+2cos⁡xsin⁡xcos⁡xsin⁡x+2cos⁡xcos⁡xsin⁡x=(sin⁡x+2cos⁡x)1cos⁡xcos⁡x1sin⁡xcos⁡x1cos⁡xsin⁡xApplying R2→R2−R1 and R3→R3−R1, we getΔ=(sin⁡x+2cos⁡x)1cos⁡xcos⁡x0sin⁡x−cos⁡x000sin⁡x−cos⁡x  =(sin⁡x+2cos⁡x)(sin⁡x−cos⁡x)2Thus, Δ=0⇒tan⁡x=−2 or tan⁡x=1As −π/4≤x≤π/4, we get −1≤tan⁡x≤1∴ tan⁡x=1⇒x=π/4