Is 1-cos^2(x)=sin(x) ?

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

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prove 1-cos^2(x)=sin(x)

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

1 - cos^{2} (1) = 0.70807 \dots

1 - cos^{2} (1)

Refine to a decimal form

= 0.70807 \dots

sin (1) = 0.84147 \dots

sin (1)

Refine to a decimal form

= 0.84147 \dots

The two sides are not equal

\Rightarrow False

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

cos^{4} (x) + sin^{4} (x) = cos (2 x)

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

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

2 sin^{2} (2 x) + cos (4 x) = 1