If a `sectheta+bt a ntheta+c=0a n dpsectheta+qtantheta+r=0,` prove that `(b r-q c)^2-(p c-a r)^2=(a q0b p)^2`

If x=ptantheta+ qsectheta and y=psectheta+qtantheta the prove that x^2-y^2=q^2-p^2 .

If pth, qth and rth terms of a HP be respectively a,b and c , has prove that (q-r)bc+(r-p)ca+(p-q)ab=0 .

If r is the ratio of the roots of the equation ax^2 + bx + c = 0 , show that (r+1)^2/r =(b^2)/(ac)

If P, Q and R are the subsets of a set A, then prove that Rxx(P^(c )uuQ^(c ))^(c )=(RxxP)nn(RxxQ) .

If alpha, beta are the rots of a x^(2)+b x+c=0 and alpha+h, beta+h are the roots of p x^(2)+q x+r=0 then h=

If a ,b ,c are in G.P. and a-b ,c-a ,a n db-c are in H.P., then prove that a+4b+c is equal to 0.

If 1/a+1/(a-b)+1/c+1/(c-b)= 0 and a + c-b!=0 , then prove that a, b, c are in H.P.

If the p^("th"), q^("th") and r^("th") terms of a G.P. are a, b and c, respectively. Prove that a^(q – r) b^(r-p) c^(P - q) = 1.

Let a ,b , c ,p ,q be real numbers. Suppose alpha,beta are the roots of the equation x^2+2p x+q=0,alphaa n d1//beta are the roots of the equation a x^2+2b x+c=0,w h e r ebeta^2 !in {-1,0,1}dot Statement 1: (p^2-q)(b^2-a c)geq0 Statement 2: b!=p aorc!=q a