Is tan^2(x)-sec^2(x)=-1 ?

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

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prove tan^2(x)-sec^2(x)=-1

prove

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

True

Solution steps

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

Use the Pythagorean identity:

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

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

\Rightarrow True

tan^{2} (θ) - sin^{2} (θ) = sin^{4} (θ) sec^{2} (θ)

cos (- θ) = cos (θ)

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

cos (\frac{5 π}{4} - x) = - \frac{2}{2} (cos (x) + sin (x))

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