Show that 1 + tan^2(x) = sec^2(x)
tan^2(x) + 1 = sin^2(x)/cos^2(x) + 1 = [sin^2(x) + cos^2(x)]/cos^2(x) = 1/cos^2(x) = (1/cos(x)^)2 = sec^2(x) Thus tan^2(x) + 1 = sec^2(x).
10^(2y) = 25, then 10^(-y) equals:
Rewriting the given expression 10^(2y) = 25 (10^y)^2 = 25 10^y = 5 1/10^y = 1/5 10^(-y) = 1/5
For what value of the constant K does the equation Kx^2 + 2x = 1 have two real solutions?
1.Rewrite the given quadratic equation in standard form: Kx^2 + 2x - 1 = 0 2.Discriminant = 4 - 4(K)(-1) = 4 + 4K 3.For the equation to have two real solutions, the discriminant has to be positive. Hence we need to solve the inequality 4 + 4K > 0. 4.The solution set to the above inequality is given by: K > -1 for which the given equation has two real solutions.