Is cos^2(θ)-sin^2(θ)=1 ?

The answer to whether cos^2(θ)-sin^2(θ)=1 is False

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prove cos^2(θ)-sin^2(θ)=1

prove

cos^{2} (θ) - sin^{2} (θ) = 1

False

Solution steps

cos^{2} (θ) - sin^{2} (θ) = 1

Show that the two sides are not equal

For

cos^{2} (θ) - sin^{2} (θ) = 1

plug in

θ = 1

cos^{2} (1) - sin^{2} (1) = - 0.41614 \dots

cos^{2} (1) - sin^{2} (1)

Refine to a decimal form

= - 0.41614 \dots

The two sides are not equal

\Rightarrow False

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

\frac{1 - tan ^{4} ( θ )}{sec ^{2} ( θ )} = 1 - tan^{2} (θ)

(1 + csc (θ)) (1 - sin (θ)) = csc (θ) - sin (θ)

\frac{2 cot ( x )}{1 + cot ^{2} ( x )} = cos (2 x)

sin^{2} (x) cos^{2} (x) = \frac{1}{8} (1 - sin (4 x))