Is csc^2(θ)-cot^2(θ)=1 ?

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

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prove csc^2(θ)-cot^2(θ)=1

prove

csc^{2} (θ) - cot^{2} (θ) = 1

True

Solution steps

csc^{2} (θ) - cot^{2} (θ) = 1

Use the Pythagorean identity:

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

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

\Rightarrow True

p ro v e (sec^{2} (x) - 1) csc^{2} (x) = sec^{2} (x)

p ro v e (1 + sin (a)) (1 - sin (a)) = cos^{2} (a)

p ro v e sin^{3} (θ) = \frac{3}{4} sin (θ) - \frac{1}{4} sin (3 θ)

p ro v e tan^{2} (θ) + 1 = sec^{2} (θ)

p ro v e \frac{cos ( x ) sec ( x )}{tan ( x )} = cot (x)