If (n+1)!=90×(n-1)!,find n.

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angelteddy033

26.09.2021

Mathematics

Remember that

$\tan\theta=\dfrac{\sin\theta}{\cos\theta}$

So if $\sin\theta0$ and $\tan\theta$ , then we know $\cos\theta$ .

Then use the Pythagorean identity to solve for cosine:

$\cos^2\theta+\sin^2\theta=1\implies\cos\theta=-\sqrt{1-\sin^2\theta}=-\dfrac{2\sqrt{10}}7$

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