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

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

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

prove

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

True

Solution steps

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

Use the Pythagorean identity:

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

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

\Rightarrow True

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

cot (a) sec (a) = csc (a)

sec^{2} (θ) + csc^{2} (θ) = sec^{2} (θ) csc^{2} (θ)

tan (\frac{x}{2}) + cot (\frac{x}{2}) = 2 csc (x)

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