cos−1⁡12x2+1−x21−x24=cos−1⁡x2−cos−1⁡x holds for

We observe thatx22+1−x21−x24 is positive and defined for all x∈[−1, 1]∴ cos−1⁡x22+1−x21−x24∈0,π2Now, RHS of the given relation is defined forx2≤1 and |x|≤1 i,e. for x∈[−1, 1]Also, LHS ≥0⇒ cos−1⁡x2−cos−1⁡x≥0⇒cos−1⁡x2≥cos−1⁡x⇒x∈[0,1]Hence, LHS = RHS for x∈[0, 1].