Solve the quadratic equation of x

(sin(2a)).x^{2}- 2.x.(sin(a)+cos(a)) +2 =0

Kindly explain your answer.

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- Aug 6th 2012, 04:08 PMlouisejaneQuadratic Equation: please sove
Solve the quadratic equation of x

(sin(2a)).x^{2}- 2.x.(sin(a)+cos(a)) +2 =0

Kindly explain your answer. - Aug 6th 2012, 04:14 PMrichard1234Re: Quadratic Equation: please sove
Rewrite $\displaystyle \sin {2a}$ as $\displaystyle 2 \sin a \cos a$ and divide everything by 2:

$\displaystyle (\sin a \cos a )x^2 - (\sin a + \cos a)x + 1 = 0$

Apparently this factors to

$\displaystyle (x \sin a - 1)(x \cos a - 1) = 0$.

Solve for x. - Aug 6th 2012, 10:22 PMlouisejaneRe: Quadratic Equation: please sove
Thanks for it Richard. I appreciate it but I still don't get it. Can you explain it further?

- Aug 6th 2012, 10:50 PMrichard1234Re: Quadratic Equation: please sove
What step don't you get?

- Aug 6th 2012, 10:54 PMlouisejaneRe: Quadratic Equation: please sove
In the substitution.

- Aug 6th 2012, 11:05 PMrichard1234Re: Quadratic Equation: please sove
Trig identity, $\displaystyle \sin 2a = 2 \sin a \cos a$ for all $\displaystyle a$.

- Aug 6th 2012, 11:13 PMlouisejaneRe: Quadratic Equation: please sove
Thanks!