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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Manipulating right side

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

Expand

(- 1 + sin (x))^{2} : 1 - 2 sin (x) + sin^{2} (x)

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

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

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

Is 2-2sin(x)-cos^2(x)=(sin(x)-1)^2 ?
The answer to whether 2-2sin(x)-cos^2(x)=(sin(x)-1)^2 is True