Show that `sin^(2)x=p+1/p` is impossible if x is real.

Show that the equation sintheta=x+1/x is not possible if x is real.

Show that the statement p: ''If x is a real number such that x^(3) + 4x = 0 , then x is 0'' is true by (i) direct method, (ii) method of contradiction, (iii) method of contrapositive

Show that the statement p: If x is a real number such that x^(3)+4x=0 , then x is 0 is true by (i) Direct method (ii) Method of contradiction (iii) Method of contrapositive

if the roots of the equation 1/ (x+p) + 1/ (x+q) = 1/r are equal in magnitude but opposite in sign, show that p+q = 2r & that the product of roots is equal to (-1/2)(p^2+q^2) .

If cos^(4)theta+p, sin^(4)theta+p are the roots of the equation x^(2)+a(2x+1)=0 and cos^(2)theta+q,sin^(2)theta+q are the roots of the equation x^(2)+4x+2=0 then a is equal to

Suppose X has a binomial distribution B(6, (1)/(2)) . Show that X = 3 is the most likely outcome. (Hint: P(X = 3) is the maximum among all P(x_(1)), x_(1)= 0,1,2,3,4,5,6 )

Show that if p,q,r and s are real numbers and pr=2(q+s) , then atleast one of the equations x^(2)+px+q=0 and x^(2)+rx+s=0 has real roots.

Show that, sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/sqrt2lexle1/sqrt2

Show that the angle between the tangent at any point P and the line joining P to the origin O is same at all points on the curve log(x^2+y^2)=ktan^(-1)(y/x)