Find the value of `a^2+1`if `a=-1`

If a^2+1/(a^2)=102 , find the value of a-1/a

Find the value of : arc sin (1/2) + arc cos (1/2)

Find the value of x if |[2, 1 ,x+1],[-1,3,-4],[0,-5,3]|=0

Find the value of tan { 1/2 sin^(-1) ((2x)/(1+x^(2))) + 1/2 cos^(-1) ((1-y^(2))/(1+ y^(2)))}

Find the value of: tan(1/2 [sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))]),|x| 0 and x y < 1

Find the value of: tan1/2[sin^(-1)(2x)/(1+x^2)+cos^(-1)(1-y^2)/(1+y^2)],|x| 0 and x y" "<" "1

If x in (0, 1) , then find the value of tan^(-1) ((1 -x^(2))/(2x)) + cos^(-1) ((1 -x^(2))/(1 + x^(2)))

If alpha and beta are the roots of the equation x^2+4x + 1=0(alpha > beta) then find the value of 1/(alpha)^2 + 1/(beta)^2

Find the value of k if k+1, 2k+1 and k+7 are in A.P.. Also find the next two terms of the A.P.

Find the value of cos^-1(-1//2) .