Rewrite with only sin x and cos x.

cos 2x + sin x

Question

Rewrite with only sin x and cos x.

cos 2x + sin x

saifoo.khan · Answer

http://openstudy.com/study#/updates/5049ec00e4b03fcc6a71baa7

anonymous · Answer

it looks like a different problem

anonymous · Answer

cos(2x)=cos²x-sin²x

anonymous · Answer

and then sin x =

anonymous · Answer

cos^2x-sin^2x=1 ... therefore, 1+sinx=0 ... sinx=-1

anonymous · Answer

@Eng.Mido  $$
\cos^2x +\sin^2x = 1
$$Not minus...

anonymous · Answer

so the answer woud be 1- 2 sin^2 x + sin x

anonymous · Answer

thanks ... I felt that sth was wrong too. :D

anonymous · Answer

cos2x=cos^2 x -sin^2x
sin2x=2sinxcosx

anonymous · Answer

$$ \begin{split}
\cos (2x) + \sin (x) &= \cos^2(x) - \sin^2(x) + \sin(x) \
&= (1-\sin^2(x))-\sin^2(x) + \sin(x) \
&= 1 - 2\sin^2(x) + \sin(x)

\end{split}
$$

anonymous · Answer

u could then take sinx as a common factor and solve the quadratic equation!!!

anonymous · Answer

Hmmm, actually we don't really need to use Pythagorean theorem here.

anonymous · Answer

@Eng.Mido Seems obvious to me that the roots are $\pi / 2$ etc.

anonymous · Answer

Hopefully $$
1 - 2\sin(x) \sin(x)+\sin(x)
$$Is good enough?

anonymous · Answer

yep i think thats it

anonymous · Answer

@wio My reply was very clear ... As I used the word "Could"!!