Is sqrt(2)sin(x+45)=sin(x)+cos(x) ?

The answer to whether sqrt(2)sin(x+45)=sin(x)+cos(x) is True

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prove sqrt(2)sin(x+45)=sin(x)+cos(x)

prove

2 sin (x + 4 5^{\circ}) = sin (x) + cos (x)

True

Solution steps

2 sin (x + 4 5^{\circ}) = sin (x) + cos (x)

Manipulating left side

2 sin (x + 4 5^{\circ})

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

4 cot (θ) = cot (θ) sin^{2} (θ)

cos (2 θ) + 1 = 2 cos^{2} (θ)

- 2 cos (x) sec^{2} (x) = - \frac{2}{cos ( x )}

1 + sin (4 a) + sin (2 a) = sin (2 a)

cot (x) sec (x) = \frac{1}{sin ( x )}

Is sqrt(2)sin(x+45)=sin(x)+cos(x) ?
The answer to whether sqrt(2)sin(x+45)=sin(x)+cos(x) is True