How do you solve $2 sin x cos x + cos x = 0$ $2sinx cosx + cosx = 0$ from 0 to 2pi?

Question

How do you solve $2 sin x cos x + cos x = 0$ $2sinx cosx + cosx = 0$ from 0 to 2pi?

1 Answer

Impact of this question

31350 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-24T10:45:23

Solution set is ${\frac{π}{2}, \frac{7 π}{6}, \frac{3 π}{2}, \frac{11 π}{6}}$ ${pi/2, (7pi)/6, (3pi)/2, (11pi)/6}$

Explanation:

In $2 sin x cos x + cos x = 0$ $2sinxcosx+cosx=0$ , taking $cos x$ $cosx$ common we get

$cos x (2 sin x + 1) = 0$ $cosx(2sinx+1)=0$

Hence,

either $cos x = 0$ $cosx=0$ whose solution in domain $[0, 2 π]$ $[0, 2pi]$ is ${\frac{π}{2}, \frac{3 π}{2}}$ ${pi/2, (3pi)/2}$

or $2 sin x + 1 = 0$ $2sinx+1=0$ i.e. $sin x = - \frac{1}{2}$ $sinx=-1/2$ whose solution in domain $[0, 2 π]$ $[0, 2pi]$ is ${\frac{7 π}{6}, \frac{11 π}{6}}$ ${(7pi)/6, (11pi)/6}$

Hence solution set is ${\frac{π}{2}, \frac{7 π}{6}, \frac{3 π}{2}, \frac{11 π}{6}}$ ${pi/2, (7pi)/6, (3pi)/2, (11pi)/6}$

Science

Math

Humanities

... and beyond

How do you solve $2 sin x cos x + cos x = 0$ $2sinx cosx + cosx = 0$ from 0 to 2pi?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve 2sinx cosx + cosx = 02sinxcosx+cosx=02sinx cosx + cosx = 0 from 0 to 2pi?

1 Answer

Explanation:

Related questions

Impact of this question

How do you solve $2 sin x cos x + cos x = 0$ $2sinx cosx + cosx = 0$ from 0 to 2pi?