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

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

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

prove

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

True

Solution steps

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

Manipulating right 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

(sin (t)) cot (t) = cos (t)

(1 - tan^{2} (x)) \cdot cos^{2} (x) = cos (2 x)

cot^{2} (x) - 1 = tan^{2} (x)

sin^{2} (θ) + 1 = - 1 - cos^{2} (x)

cos (θ) = 1 - sin^{2} (θ)

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