Can anyone please explain to me what exactly was done in the encircled two lines and why? I've tried figuring it out but I just can't make any sense of it.
Thank you for your time. Photo
2026-04-04 13:40:22.1775310022
Trigonometric functions in system of equations
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I think you have added the two equations: \begin{align}c_2^{'}(x)\cos^2x&=\sin x \cos^2x \tag{1}\\ c_2^{'}(x)\sin^2x&=0 \tag{2} \end{align} Now, add them; $$c_2^{'}(x)[\cos^2x+\sin^2x]=\sin x \cos^2x.$$ Since, $\cos^2x+\sin^2x=1$, you get $c_2^{'}(x)=\sin x \cos^2x$.