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

The answer to whether 1-csc^2(x)=-cot^2(x) is True

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

prove

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

True

Solution steps

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

Use the Pythagorean identity:

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

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

\Rightarrow True

sec (x) + sec^{2} (x) = 2

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

tan (x) = tan (x) \cdot csc^{2} (x) + cot (- x)

sin (θ) cos (θ) csc^{2} (θ) = cot (θ)

csc (2 θ) = \frac{1 + tan ^{2} ( θ )}{2 tan ( θ )}