limx→0 log⁡log⁡1−x2log⁡log⁡cos⁡x is equal to

we have ,limx→0 log⁡log⁡1−x2log⁡log⁡cos⁡x ( form ∞/∞)=limx→0 1log⁡1−x2⋅11−x2⋅(−2x)1log⁡cos⁡x⋅1cos⁡x⋅(−sin⁡x)=2limx→0 xcos⁡xlog⁡cos⁡xsin⁡x⋅1−x2log⁡1−x2=2limx→0 xsin⁡x⋅limx→0 cos⁡x1−x2⋅limx→0 log⁡cos⁡xlog⁡1−x2=2×1×1×limx→0 log⁡cos⁡xlog⁡1−x2  (from 0/0)=2limx→0 1cos⁡x⋅(−sin⁡x)11−x2⋅(−2x)=2×12⋅limx→0 sin⁡xx⋅1−x2cos⁡x=1