What is sin^3(x)(1+cot^2(x))-(1-cos^2(x))csc(x) ?

The solution to sin^3(x)(1+cot^2(x))-(1-cos^2(x))csc(x) is 0

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simplify sin^3(x)(1+cot^2(x))-(1-cos^2(x))csc(x)

simplify

sin^{3} (x) (1 + cot^{2} (x)) - (1 - cos^{2} (x)) csc (x)

0

Solution steps

sin^{3} (x) (1 + cot^{2} (x)) - (1 - cos^{2} (x)) csc (x)

1 + cot^{2} (x) = csc^{2} (x)

(1 - cos^{2} (x)) csc (x) = sin^{2} (x) csc (x)

= sin^{3} (x) csc^{2} (x) - sin^{2} (x) csc (x)

csc (x) sin (x) = 1

= sin^{2} (x) csc (x) (- 1 + 1)

Factor

sin^{3} (x) csc^{2} (x) - sin^{2} (x) csc (x) : sin^{2} (x) csc (x) (sin (x) csc (x) - 1)

= sin^{2} (x) csc (x) (sin (x) csc (x) - 1)

= 0

6 sin (x) cos (x)

r^{2} cos^{2} (θ) + r^{2} sin^{2} (θ)

9 \cdot \frac{3}{4}

\frac{14}{40}

lo g_{\frac{1}{5}} (\frac{1}{125})

What is sin^3(x)(1+cot^2(x))-(1-cos^2(x))csc(x) ?
The solution to sin^3(x)(1+cot^2(x))-(1-cos^2(x))csc(x) is 0