Is sec^2(θ)-tan^2(θ)=1 ?

The answer to whether sec^2(θ)-tan^2(θ)=1 is True

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prove sec^2(θ)-tan^2(θ)=1

prove

sec^{2} (θ) - tan^{2} (θ) = 1

True

Solution steps

sec^{2} (θ) - tan^{2} (θ) = 1

Use the Pythagorean identity:

sec^{2} (x) = tan^{2} (x) + 1

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

\Rightarrow True

\frac{1 + tan ^{2} ( x )}{tan ^{2} ( x )} = csc^{2} (x)

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

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

csc (θ) sec (θ) - cot (θ) = tan (θ)

1 - tan^{2} (\frac{θ}{2}) = \frac{2 cos ( θ )}{1 + cos ( θ )}