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

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

sin (θ) csc (θ) = 1

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

(sin (x) + cos (x))^{2} = sin (2 x) + 1

\frac{tan ( θ )}{sec ( θ )} = sin (θ)