glorp

[floral walrus]

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[near gorge]

second equality should be clear

[spiral gust]

They're combining the cos(θ)-sin(θ) into one term by using the difference of cos(a)cos(b)-sin(a)sin(b)

[near gorge]

it's an algebraic trick basically

multiplying the expression by 1 in a clever fashion

[spiral gust]

Here a= θ and b=π/4, since cos(b)=sin(b) for that b, then they multiply in front with sqrt of 2 to account for the cos(π/4)=1/sqrt(2)

[near gorge]

$$ \cos \theta - \sin \theta = \sqrt{2} \left( \frac{\sqrt{2}}{2}\cos \theta - \frac{\sqrt{2}}{2}\sin \theta\right) $$

[loud remnant]

aL

[near gorge]

@ember zealot