Is 2sin^2(45)=1-cos(90) ?

The answer to whether 2sin^2(45)=1-cos(90) is True

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prove 2sin^2(45)=1-cos(90)

prove

2 sin^{2} (4 5^{\circ}) = 1 - cos (9 0^{\circ})

True

Solution steps

2 sin^{2} (4 5^{\circ}) = 1 - cos (9 0^{\circ})

Manipulating left side

2 sin^{2} (4 5^{\circ})

Simplify

2 sin^{2} (4 5^{\circ}) : 1

= 1

Manipulating right side

1 - cos (9 0^{\circ})

Simplify

1 - cos (9 0^{\circ}) : 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

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cot (θ) - tan (θ) = 2 cot (2 θ)

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

cot (2 x) = \frac{sec ( x ) + csc ( x )}{2 sin ( x ) - 2 cos ( x )}

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