Find the set of values of parameter `a` so that the equation `(sin^(-1)x)^3+(cos^(-1)x)^3=api^3` has a solution.

Find the set of values of parameter a so that the equation (sin^(-1)x)^(3)+(cos^(-1)x)^(3)=a pi^(3) has a solution.

Find the set of value of 'a' for which the equation 2 cos^(-1) x=a +a^(2) (cos^(-1) x)^(-1) posses a solution.

Prove that the equation 3(sin x+cos x)-2(sin^(3)x+cos^(3)x)=8 has no solution.

Find the range of lambda so that the equation sin^(6)x+cos^(6)x=lambda-1 has a real solution.

Find the range of lambda so that the equation sin^(6)x+cos^(6)x=lambda-1 has a real solution.

Find the set of values of a for which the equation 2cos^-1 x = a+a^2(cos^-1 x)^-1 posses a solution