What is sin^3(x)csc(x)+cos^3(x)sec(x) ?

The solution to sin^3(x)csc(x)+cos^3(x)sec(x) is sin^2(x)+cos^3(x)sec(x)

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simplify sin^3(x)csc(x)+cos^3(x)sec(x)

simplify

sin^{3} (x) csc (x) + cos^{3} (x) sec (x)

sin^{2} (x) + cos^{3} (x) sec (x)

Solution steps

sin^{3} (x) csc (x) + cos^{3} (x) sec (x)

Use the basic trigonometric identity:

csc (x) = \frac{1}{sin ( x )}

= \frac{1}{sin ( x )} sin^{3} (x)

Simplify

\frac{1}{sin ( x )} sin^{3} (x) : sin^{2} (x)

= sin^{2} (x) + cos^{3} (x) sec (x)

x^{2} - \frac{2}{3} x + \frac{1}{9}

\frac{52}{13}

6 \times \frac{2}{3}

4 x^{2} - 24 x - 160

(3 x + 2) (2 x + 1)

What is sin^3(x)csc(x)+cos^3(x)sec(x) ?
The solution to sin^3(x)csc(x)+cos^3(x)sec(x) is sin^2(x)+cos^3(x)sec(x)