Explain the fallacy in the following:` -1=i.i=sqrt(-1).sqrt(-1)=sqrt((-1)(-1))=sqrt(1)=1`

Evaluate the following: (sqrt(x+1)+sqrt(x-1))^6+(sqrt(x+1)-sqrt(x-1))^6

If sqrt(2)=1.414,sqrt(3)=1.732 , find the value of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)" "(ii)(sqrt(3)-1)/(sqrt(3)+1)" "(iii)(2+sqrt(6))/(sqrt(2))

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))

Which of the following is equal to root(3)(-1) a. (sqrt(3)+sqrt(-1))/2 b. (-sqrt(3)+sqrt(-1))/(sqrt(-4)) c. (sqrt(3)-sqrt(-1))/(sqrt(-4)) d. -sqrt(-1)

x=sqrt(1+2sqrt(1+3sqrt(1+4sqrt(1+...

Differentiate the following function (sqrt(x^2+1)+sqrt(x^2-1))/(sqrt(x^2+1)-sqrt(x^2-1)

Find the principal value of each of the following: (i) tan^(-1)(1/(sqrt(3))) (ii) tan^(-1)(-1/(sqrt(3)))

Find the principal values of the following : (i) sin^(-1)(sqrt(-3/2)) (ii) cot^(-1)(-sqrt(3)) (iii) cos^(-1)(-1(1)/(2)) (iv) sec^(-1)(-(2)/sqrt(3)) (v) tan^(-1)(-1) (vi) cosec ^(-1)(-1) .

Find the principal value of the following (i) sin^(-1).(1)/(2) (ii) tan ^(-1).(1)/sqrt(3) (iii) cot ^(-1)(-sqrt3)

For the principal values, evaluate each of the following : (i) sin^(-1)(-1/2)+2cos^(-1)(-(sqrt(3))/2) (ii) sin^(-1)(-(sqrt(3))/2)+cos^(-1)((sqrt(3))/2)