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  • If m and M are the least and the greatest value of (cos ^-1 x)^2+(sin^-1x)^2 , then M/m=?

If m and M are the least and the greatest value of (cos ^-1 x)^2+(sin^-1x)^2 , then M/m=?

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Solution:     We have ,     (cos^-1x)^2+(sin^-1x)^2

                (fracpi2-sin^-1x)^2+(sin^-1x)^2=fracpi^28+2[sin^-1x-fracpi4]^2

                 m=fracpi^28,M=frac5pi^24Rightarrow fracMm=10.

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Deependra Verma

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