evaluate: cot(arcsin(1/(x-1)))

Question

anonymous · Answer

So, I like to think of these problems as saying: Some triangle has a sin of 1/(x-1). What is the cotangent of that SAME triangle.

anonymous · Answer

So we start off by drawing a triangle that has a sin of 1/(x-1). Because sin is opposite side over hypotenuse, the 1 becomes the opposite and the x-1 becomes the hypotenuse. 

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Now you just need to find that missing side and get the cotangent, which would be the adjacent side over the opposite side

anonymous · Answer

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like that

anonymous · Answer

$$\sqrt{(x-1)^{2}-1^{2}}$$

anonymous · Answer

2x-x^2?

anonymous · Answer

$$\sqrt{(x-1)^{2}-1^{2}} \implies \sqrt{x^{2}-2x+1-1} \implies \sqrt{x^{2}-2x}$$This is just foiling out the inside properly and cancelling the ones inside. So this would be your missing adjacent side.

anonymous · Answer

ohhh I get it thanks im an idiot haha

anonymous · Answer

Lol, no worries. Glad ya got it :3