How do you simplify ${sin}^{2} x {csc}^{2} x - {sin}^{2} x$ $sin^2x csc^2x - sin^2x$ ?

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How do you simplify ${sin}^{2} x {csc}^{2} x - {sin}^{2} x$ $sin^2x csc^2x - sin^2x$ ?

1 Answer

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Answer 1 · 2015-09-03T21:46:01

The expression simplifies into ${cos}^{2} (x)$ $cos^2(x)$

Explanation:

You only need to write down the definitions: since $csc (x) = \frac{1}{sin (x)}$ $csc(x)=1/{\sin(x)}$ , we have that

${sin}^{2} (x) \cdot {csc}^{2} (x) - {sin}^{2} (x) = \frac{{sin}^{2} (x)}{{sin}^{2} (x)} - {sin}^{2} (x)$ $\sin^2(x) * csc^2(x) - \sin^2(x) = {\sin^2(x)}/{\sin^2(x)} - \sin^2(x)$

The first term is obviously $1$ $1$ , so you have $1 - {sin}^{2} (x)$ $1-\sin^2(x)$ , which equals ${cos}^{2} (x)$ $\cos^2(x)$ because of the fundamental formula ${cos}^{2} (x) + {sin}^{2} (x) = 1$ $\cos^2(x)+\sin^2(x)=1$

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How do you simplify ${sin}^{2} x {csc}^{2} x - {sin}^{2} x$ $sin^2x csc^2x - sin^2x$ ?

1 Answer

Explanation:

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How do you simplify sin^2x csc^2x - sin^2xsin2xcsc2x−sin2xsin^2x csc^2x - sin^2x?

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How do you simplify ${sin}^{2} x {csc}^{2} x - {sin}^{2} x$ $sin^2x csc^2x - sin^2x$ ?