Is cot^2(x) 1/(csc(x))=csc^2(x) ?

The answer to whether cot^2(x) 1/(csc(x))=csc^2(x) is False

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prove cot^2(x) 1/(csc(x))=csc^2(x)

prove

cot^{2} (x) \frac{1}{csc ( x )} = csc^{2} (x)

False

Solution steps

cot^{2} (x) \frac{1}{csc ( x )} = csc^{2} (x)

Show that the two sides are not equal

For

cot^{2} (x) \frac{1}{csc ( x )} = csc^{2} (x)

plug in

x = 1

cot^{2} (1) \frac{1}{csc ( 1 )} = 0.34692 \dots

cot^{2} (1) \frac{1}{csc ( 1 )}

Refine to a decimal form

= 0.34692 \dots

csc^{2} (1) = 1.41228 \dots

csc^{2} (1)

Refine to a decimal form

= 1.41228 \dots

The two sides are not equal

\Rightarrow False

(tan (x)) (1 - cot (x)) = tan (x) - 1

tan^{2} (x) - sin^{2} (x) = tan^{2} (x)

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

\frac{1}{tan ^{2} ( x )} = \frac{cos ^{2} ( x )}{sin ^{2} ( x )}

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

Is cot^2(x) 1/(csc(x))=csc^2(x) ?
The answer to whether cot^2(x) 1/(csc(x))=csc^2(x) is False