the value of `cos(cos^-1x+sin^-1(x-2))` is equal to (A) 0 (B) 1 (C) -1 (D) `sqrt(1-x^2).sqrt(x^2-4x+3) +x (x-2)`

The value of cos(2cos^-1x+sin^-1x) at x= 1/5 is (A) 1 (B) 3 (C) 0 (D) (-2sqrt(6))/5

The value of cos [ tan^-1 {sin (cot^-1 (x))}] is a) sqrt((x^2+1)/(x^2-1)) b) sqrt((1-x^2)/(x^2+2)) c) sqrt((1-x^2)/(1+x^2)) d) sqrt((x^2+1)/(x^2+2))

"tan"(cos^(-1)x) is equal to x/(1+x^2) b. (sqrt(1+x^2))/x c. (sqrt(1-x^2))/x d. sqrt(1-2x)

tan(cos^(-1)x) is equal to (x)/(1+x^(2)) b.(sqrt(1+x^(2)))/(x) c.(sqrt(1-x^(2)))/(x) d.sqrt(1-2x)

lim_(x->oo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) 0 (b) 1 (c) 1/3 (d) 1/2

"tan"(cos^(-1)x) is equal to a. x/(1+x^2) b. (sqrt(1+x^2))/x c. (sqrt(1-x^2))/x d. sqrt(1-2x)

("lim")_(xvecoo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) 0 (b) 1 (c) 1/3 (d) 1/2

("lim")_(xvecoo)(sin^4x-sin^2x+1)/(cos^4x-cos^2x+1) is equal to (a) 0 (b) 1 (c) 1/3 (d) 1/2

If 0lt xlt1 , then sqrt(1+x^2)[{cos (cot^(-1)x)+sin(cot^(-1)x)}^(2)-1]^(1//2) is equal to a) x/sqrt(1+x^2) b)x c) xsqrt(1+x^2) d) sqrt(1+x^2)

d/(dx)(sin^(-1)x+cos^(-1)x) is equal to : (A) (1)/(sqrt(1-x^(2))), (B) (2)/(sqrt(1-x^(2))), (C) 0 (D) sqrt(1-x^(2))