## koli123able 2 years ago Show that the function sinx+cosx is of period 2pi. Also prove that sinx+cosx=sqrt(2)sin(x+pi/4)

1. yashar806

hi satellite help me after this

2. goformit100

i think it is C.B.S.E. Question

3. koli123able

$\sqrt2\sin(x+\frac{ \pi }{ 4 })$

4. koli123able

what does C.B.S.E means ?

5. koli123able

sinx cos pi/4 + cosx sin pi/4 what's next?

6. satellite73

it is a consequence of the "addition angle" formula the general case is $a\sin(x)+b\cos(x)=\sqrt{a^2+b^2}\sin(x+\theta)$ and a succinct explanation is in the attachment

7. campbell_st

this requires putting into the form asin(x) + bcos(x) = Rsin(x + m) $R = \sqrt{a^2 + b^2}$ and $m = \tan^{-1}(\frac{a}{b})$ so$R = \sqrt{1^2 + 1^2 } = \sqrt{2}$ $m = \tan^{-1}(\frac{1}{1}) = \frac{\pi}{4}$ so you get $\sqrt{2}\sin(x + \frac{\pi}{4})$