cos(a^(2)+sqrt(a^(2)-1))^(4)+{a^(2)-sqrt(a^(2)-1)}^(4)

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

Show 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) .

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

sin ^(-1)[cot ((sin ^(-1) sqrt((2-sqrt(3))/(4)))+cos ^(-1) (sqrt(12))/(4)+sec ^(-1) sqrt(2))]

(d)/(dx)[cos^(-1)(x sqrt(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.1/4c.-1/4d none of these

The area enclosed by the curve y=sin x+cos x and y=|cos x-sin x| over the interval [0,(pi)/(2)] is 4(sqrt(2)-2) (b) 2sqrt(2)(sqrt(2)-1)2(sqrt(2)+1)(d)2sqrt(2)(sqrt(2)+1)

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