Suppose that `a costheta= b` and `c sintheta=d`, for and some constants `a, b, c, d.` Then which of the following is true? (1) `a^2c^2=b^2c^2+a^2d^2`(2)`a^2d^2=b^2c^2+a^2c^2`

If the integers a,b,c,d are in A.P a

If a,b,c,d are in continued proportion then show that (b-c)^2+(c-a)^2+(b-d)^2= (a-d)^2 .

If a, b, c and d are in G.P. show that (a^2+b^2+c^2)(b^2+c^2+d^2)=(a b+b c+c d)^2 .

If a, b, c and d are in G.P. show that (a^2+b^2+c^2)(b^2+c^2+d^2)=(a b+b c+c d)^2 .

If a ,\ b ,\ c ,\ d are in G.P., show that: (a b+b c+c d)^2=(a^2+b^2+c^2)(b^2+c^2+d^2)

If a, b, c and d are in G.P. show that (a^2+b^2+c^2)(b^2+c^2+d^2)=(a b+b c+c d)^2 .

Comprehension (For Q.No.1 to 3) Let f(x)=x^2+2a x+b ,g(x)=c x^2+2dx+1 be quadratic expressions whose graph is a as shown in the figure. Here it is given that |A A^'|=|B B^'|a n d|O A^'|=|O B| Which of the following statements is correct a^2+d=d^2+c (b) a+d=b+c a^2+d^2=c+b (d) b c+c+a^2c+d^2

Let f(x)=x^2+2a x+b ,g(x)=c x^2+2dx+1 be quadratic expressions whose graph is a as shown in the figure. Here it is given that |A A^'|=|B B^'|a n d|O A^'|=|O B| Which of the following statements is correct a^2+d=d^2+c (b) a+d=b+c a^2+d^2=c+b (d) b c+c+a^2c+d^2

If a, b, c, d are in G.P., then prove that: (b-c)^(2)+(c-a)^(2)+(d-b)^(2)=(a-d)^(2)

If a,b,c,d are in G.P then show that (b-c)^2+(c-a)^2+(d-b)^2=(a-d)^2 .