SOLUTION: simplify tan²x(csc²x-1)
simplify sinxcos²x-sinx
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Question 198052: simplify tan²x(csc²x-1)
simplify sinxcos²x-sinx
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
(\csc^2(x))\ =\ \left(\frac{\sin^2(x)}{\cos^2(x)}\right)\left(\frac{1}{\sin^2(x)}-1\right)\ =\ \left(\frac{\sin^2(x)}{\cos^2(x)}\right)\left(\frac{1 - \sin^2(x)}{\sin^2(x)}\right)\ =\ \left(\frac{\sin^2(x)}{\cos^2(x)}\right)\left(\frac{\cos^2(x)}{\sin^2(x)}\right) \ =\ 1)
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\cos^2(x) - \sin(x)\ =\ \sin(x)\left(\cos^2(x) - 1\right)\ =\ \sin(x)\left(-sin^2(x)\right)\ =\ -\sin^3(x))
John
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