`cos^(-1)x = tan^(-1)x`, then: a. `x^2=((sqrt(5)-1)/2)` b. `x^2=((sqrt(5)+1)/2)` c. `sin(cos^(-1)x)=((sqrt(5)-1)/2)` d. `tan(cos^(-1)x)=((sqrt(5)-1)/2)`

then -x^(2)=((sqrt(5)-1)/(2)) b.x^(2)=((sqrt(5)+1)/(2)) c.sin(cos^(-1)x)=((sqrt(5)-1)/(2))dtan(cos^(-1)x)=((sqrt(5)-1)/(2))

Solve for x, if : tan (cos^(-1)x)=(2)/(sqrt(5))

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

tan (sec ^ (- 1) x) = sin (cos ^ (- 1) ((1) / (sqrt (5))))

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

If x takes negative permissible values , then sin^(-1) x= a) cos^(-1)sqrt(1-x^2) b) -cos^(-1)sqrt(1-x^2) c) cos^(-1)sqrt(x^2-1) d) pi-cos^(-1)sqrt(1-x^2)

If tan(cos^(-1)x)="sin"(cot^(-1)(1/2)) then x is equal to- a. 1/sqrt(5) b. 2/sqrt(5) c. 3/sqrt(5) d. sqrt(5)/3

If tan(cos^(-1)x)="sin"(cot^(-1)(1/2)) then x is equal to- a. 1/sqrt(5) b. 2/sqrt(5) c. 3/sqrt(5) d. sqrt(5)/3

If int(dx)/(cos^(3)x sqrt(sin2x))=a(tan^(2)x+b)sqrt(tan x)+c, then (a) a=(sqrt(2))/(5),b=(1)/(sqrt(5))(b)a=(sqrt(2))/(5),b=5(c)a=(sqrt(2))/(5),b=-(1)/(sqrt(5))(d)a=(sqrt(2))/(5),b=sqrt(5)

If I=int(sin x+sin^(3)x)/(cos2x)dx=P cos x+Q log|f(x)|+R then (a)P=(1)/(2),Q=-(3)/(4sqrt(2))(b)P=(1)/(4),Q=(1)/(sqrt(2)) (c) f(x)=(sqrt(2)cos x+1)/(sqrt(2)cos x-1)(d)f(x)=(sqrt(2)cos x-1)/(sqrt(2)cos x+1)