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

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

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

prove

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

True

Solution steps

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

Manipulating left side

(1 + csc (x)) (1 - csc (x))

Expand

(1 + csc (x)) (1 - csc (x)) : 1 - csc^{2} (x)

= 1 - csc^{2} (x)

Use the Pythagorean identity:

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

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

= - cot^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

cot (u) = \frac{1}{tan ( u )}

- sin (2 x) = - 4 cos (x) sin (x)

cos (θ) (tan (θ) - sec (- θ)) = sin (θ) - 1

cos (\frac{π}{2}) = - 0

cos (x) + 1 = sin (2 x)

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