Solve : X^2+X COT A COS A-1=0.For given X, X is an acute angle.The sum of roots is?

Question

(a)SIN A-TAN A
(b)SIN A-COSEC A
(c) COS A + SEC A
(d)COSEC A-SIN A

explain it clearly.

Answer 1

The sum of the roots is the opposite of the middle term of the quadratic. In this case: - cot(A)*cos(A).

Now use some trig identities: -cos^2(A)/sin(A) = -(1 - sin^2(A))/sin(A) = -csc(A) + sin(A).

So the answer is (b).

A very odd question...

Answer 2

The sum of the roots of a quadratic equation ax^2+bx+c=0 is simply -b/a.
In your equation a = 1 and b= cotAcosA
Thus sum of roots = - cotAcosA

This is not one of the given answers, so either your book is wrong, or you have made a mistake in writing the problem.

Answer 3

sin x cos x-sin x -cos x + a million=0 sinx(cosx-a million) - (cosx-a million)=0 (cosx-a million)(sinx-a million)=0 cosx-a million =0 or sinx-a million=0 cosx = a million or sinx = a million x = 2n? or x = n? +(-a million)^n (?/2) ; n = 0,a million, 2, 3, ... Sustitute for n & discover for x interior of 0?x?? whilst n=0 ; x = 0, ?/2 interior of 0?x?? Now you will see the answer