Given,
f(x)=(sin−1x)2−(cos−1x)2=(sin−1x+cos−1x)(sin−1x−cos−1x)=π2(sin−1x−(π2−sin−1x))∴f(x)=π2(2sin−1x−π2),∀ x∈[−1,1]
As f is increasing function,
so, fmax=f(1)=π2(2(π2)−π2)=π24
and fmin=f(−1)=π2(2(−π2)−π2)=−3π24
Hence, range of f is[−3π24,π24]
∴a=−3 and b=1
∴b−a=1−(−3)=4