Is 1/(csc^2(x))=1-sin^2(x) ?

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

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prove 1/(csc^2(x))=1-sin^2(x)

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

\frac{1}{csc ^{2} ( 1 )} = 0.70807 \dots

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

Refine to a decimal form

= 0.70807 \dots

1 - sin^{2} (1) = 0.29192 \dots

1 - sin^{2} (1)

Refine to a decimal form

= 0.29192 \dots

The two sides are not equal

\Rightarrow False

sin^{4} (x) = (sin^{2} (x))^{2}

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

\frac{cot ( α )}{cos ( α )} = csc (α)

cos^{(2)} (θ) (1 + tan^{(2)} (θ)) = 1

1 - 2 sin^{2} (y) + sin^{4} (y) = cos^{4} (y)

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