Question

sin(pi/4+x)=2sqrt(2)(cosx+sinx)

Answer 1

prove the identity. really need help

Answer 2

\(\large\color{black}{ \displaystyle \sin\left(\frac{\pi}{4}+x\right)=\sin\left(\frac{\pi}{4}\right)\cos(x) +\sin(x)\cos\left(\frac{\pi}{4}+x\right) }\)

\(\large\color{black}{ \displaystyle =\sin\left(45^\circ\right)\cos(x) +\sin(x)\cos\left(45^\circ\right) }\)


and \(\large\color{black}{ \displaystyle \cos\left(45^\circ\right)=\sin\left(45^\circ\right)=\frac{\sqrt{2}}{2} }\)

Answer 3

go on...

Answer 4

just the left side?

Answer 5

sqrt2/2cosx+sinxsqrt2/2

Answer 6

you know the value of cosine and sine of 45 degrees.
So use that, and then factor the expression.

Answer 7

thank you so much I've got it now (:

Answer 8

very good