`cos^(-1){1/2x^(2)+sqrt(1+x^(2))sqrt(1-x^(2))/(4)}=cos^(-1)(x)/(2)-cos^(-1)x`

f(x)=cos^(-1)(x^(2)/sqrt(1+x^(2)))

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

Prove that tan^(-1)[(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2))]=pi/4+1/2cos^(-1)x^2

If x<0,t h e ntan^(-1)x is equal to -pi+cot^(-1)1/x (b) sin^(-1)x/(sqrt(1+x^2)) -cos^(-1)1/(sqrt(1+x^2)) (d) -cos e c^(-1)(sqrt(1+x^2))/x

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

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

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

int_(-1/sqrt3)^(-1/sqrt3)(x^4)/(1-x^4)cos^(- 1)((2x)/(1+x^2))dx

d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) (-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2))+1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2)) 0 b. 1//4 c. -1//4 d. none of these

If sin^(-1)x_i in [0,1]AAi=1,2,3, .28 then find the maximum value of sqrt(sin^(-1)x_1)sqrt(cos^(-1)x_2)+sqrt(sin^(-1)x_2)sqrt(cos^(-1)x_3)+ sqrt(sin^(-1)x_3)sqrt(cos^(-1)x_4)++sqrt(sin^(-1)x_(28))sqrt(cos^(-1)x_1)