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cos^(-1)sqrt(x)...

cos^(-1)sqrt(x)

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The value of int(sin^-1sqrt(x)-cos^-1sqrt(x))/(sin^-1sqrt(x)+cos^-1sqrt(x))dx is equal to

Evaluate int(sin^-1sqrt (x)-cos^-1sqrt (x))/(sin^-1sqrt (x)+cos^-1sqrt (x))dx

int(1)/(cos^(-1)x.sqrt(1-x^(2)))dx=

int(1)/(cos^(-1)x.sqrt(1-x^(2)))dx=

sin^(-1)x=cos^(-1)sqrt(1-x^(2))

Prove that sin^(-1)x=cos^(-1) sqrt(1-x^2)

(d)/(dx)cos^(-1)sqrt(cos x) is equal to

cos^(-1)sqrt(1-x)+sin^(-1)sqrt(1-x)=

cos^(-1){sqrt((1+x)/(2))}