What is 5csc^2(-5-2csc(x)+2) ?

The solution to 5csc^2(-5-2csc(x)+2) is 5csc^2((-2-3sin(x))/(sin(x)))

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simplify 5csc^2(-5-2csc(x)+2)

simplify

5 csc^{2} (- 5 - 2 csc (x) + 2)

5 csc^{2} (\frac{- 2 - 3 sin ( x )}{sin ( x )})

Solution steps

5 csc^{2} (- 5 - 2 csc (x) + 2)

Rewrite using trig identities

= 5 \frac{1}{sin ( - \frac{2}{s i n ( x )} - 3 )}^{2}

Simplify

5 \frac{1}{sin ( - \frac{2}{s i n ( x )} - 3 )}^{2} : \frac{5}{sin ^{2} ( \frac{- 2 - 3 s i n ( x )}{s i n ( x )} )}

= \frac{5}{sin ^{2} ( \frac{- 2 - 3 s i n ( x )}{s i n ( x )} )}

Use the basic trigonometric identity:

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

= 5 csc^{2} (\frac{- 2 - 3 sin ( x )}{sin ( x )})

- 1 + 2 cos (π - 2 x)

2 sin (u + \frac{π}{3})

tan (arctan (x) + \frac{π}{4})

sin (15 0^{\circ} - x)

1 - sin (- x)

What is 5csc^2(-5-2csc(x)+2) ?
The solution to 5csc^2(-5-2csc(x)+2) is 5csc^2((-2-3sin(x))/(sin(x)))