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

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

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

prove

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

True

Solution steps

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

Manipulating left side

2 cos (x - \frac{π}{4})

Rewrite using trig identities

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

Simplify

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

= cos (x) + sin (x)

We showed that the two sides could take the same form

\Rightarrow True

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

7 csc^{2} (θ) - 5 cot^{2} (θ) = 2 csc^{2} (θ) + 5

cos (θ) = \frac{cot ( θ )}{csc ( θ )}

\frac{cos ( u )}{1 - sin ( u )} = sec (u) + tan (u)

cos (x - \frac{3 π}{2}) = - sin (x)

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