Is coth^2(x)-csch^2(x)=1 ?

The answer to whether coth^2(x)-csch^2(x)=1 is True

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prove coth^2(x)-csch^2(x)=1

prove

coth^{2} (x) - csch^{2} (x) = 1

True

Solution steps

coth^{2} (x) - csch^{2} (x) = 1

Use the Hyperbolic identity:

csch^{2} (x) = coth^{2} (x) - 1

csch^{2} (x) - coth^{2} (x) = - 1

\Rightarrow True

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

\frac{( csc ^{2} ( x ) )}{cot ( x )} = csc (x) sec (x)

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

sin (x) cos (x) + sin (3 x) sec (x) = tan (x)

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