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I am working on trigonometric identities and my book gives me LHS = RHS and I confused as to what is going on. My answer does not match up what what It shows me. Can someone clarify what the middle term in between LHS and RHS is?


$$ \frac{sinΘ}{tanΘ} = cosΘ $$

My Work

$$ \frac{sinΘ}{\frac{sinΘ}{cosΘ}} = cosΘ $$

$$ cosΘ = cosΘ $$

Real Answer

$$ LHS = sinΘ\frac{cosΘ}{sinΘ} = RHS $$

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up vote 0 down vote accepted

Book's solution is same as what you have done(only representation is different).

your solution is L.H.S.=$$\frac{\sin\theta}{\tan\theta}=\frac{\sin\theta}{\frac{\sin\theta}{\cos\theta}}$$ which is indeed equal to $$\frac{\sin\theta\cos\theta}{\sin\theta}=\cos\theta$$=R.H.S.

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Sorry if I dont fully understand but how do you go from $ \frac{\sin\theta}{\frac{\sin\theta}{\cos\theta}}$ to $\frac{sinθcosθ}{sinθ}$ – sam Jan 24 '13 at 10:17
In arithmetic, $\frac{a}{\frac{b}{c}}=\frac{ac}{b}$ because dividing by something like $x$ is same as multiplying by its inverse $\frac{1}{x}$. So, in $\frac{a}{\frac{b}{c}}$, $a$ is being divided by $\frac{b}{c}$ which is equivalent to multiplying $a$ with inverse of $\frac{b}{c}$ which is $\frac{c}{b}$ which gives us $\frac{a}{\frac{b}{c}}=\frac{ac}{b}$ – Aang Jan 24 '13 at 10:18
thanks i see now :) – sam Jan 24 '13 at 10:21

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