Question

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

Answer 1

hi
satellite help me after this

Answer 2

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

Answer 3

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

Answer 4

what does C.B.S.E means ?

Answer 5

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

Answer 6

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

Answer 7

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

\[\sqrt{2}\sin(x + \frac{\pi}{4})\]