I have an example:
$$ \frac{49}{64}\cos^2 \theta + \cos^2 \theta = 1 $$
Then what happens next:
$$ \frac{113}{64}\cos^2 \theta = 1 $$
Where has the other cosine disappeared to? What operation happened here? Any hints please.
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Sign up to join this communityI have an example:
$$ \frac{49}{64}\cos^2 \theta + \cos^2 \theta = 1 $$
Then what happens next:
$$ \frac{113}{64}\cos^2 \theta = 1 $$
Where has the other cosine disappeared to? What operation happened here? Any hints please.
This is a simple use of the distributive law (Wikipedia link): $$ac+bc=(a+b)c$$ In this situation, $$\left(\frac{49}{64}\right)\cos^2(\theta)+\left(1\right)\cos^2(\theta)=\left(\frac{49}{64}+1\right)\cos^2(\theta)=\left(\frac{113}{64}\right)\cos^2(\theta)$$
By distributive law, $$\frac{49}{64}\cos^2 \theta+\cos^2 \theta=\left(\frac{49}{64}+1\right)\cos^2 \theta=\left(\frac{49}{64}+\frac{64}{64}\right)\cos^2 \theta=\left(\frac{49+64}{64}\right)\cos^2 \theta.$$ and the numerator $$49+64=113.$$
$\dfrac{49}{64}\cos^2 \theta + \cos^2 \theta = \left(\dfrac{49}{64} +1\right) \cos^2 \theta = \dfrac{113}{64}\cos^2 \theta$