Is sqrt(2)sin(x+pi/4)=sin(x)+cos(x) ?

The answer to whether sqrt(2)sin(x+pi/4)=sin(x)+cos(x) is True

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prove sqrt(2)sin(x+pi/4)=sin(x)+cos(x)

prove

2 sin (x + \frac{π}{4}) = sin (x) + cos (x)

True

Solution steps

2 sin (x + \frac{π}{4}) = sin (x) + cos (x)

Manipulating left side

2 sin (x + \frac{π}{4})

Rewrite using trig identities

= 2 \frac{2 sin ( x ) + 2 cos ( x )}{2}

Simplify

2 \frac{2 sin ( x ) + 2 cos ( x )}{2} : sin (x) + cos (x)

= sin (x) + cos (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{csc ( x ) + 1}{csc ( x )} = 1 + sin (x)

cos (x + x) = cos^{2} (x) - sin^{2} (x)

\frac{sin ( x )}{3 sin ( 2 x )} = \frac{1}{2 cos ( x )}

sin (x) tan (x) = 2 sec (x)

(tan (a)) (cos (a)) = sin (a)

Is sqrt(2)sin(x+pi/4)=sin(x)+cos(x) ?
The answer to whether sqrt(2)sin(x+pi/4)=sin(x)+cos(x) is True