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

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

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

prove

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

True

Solution steps

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

Manipulating right side

2 - 2 sin^{2} (x)

Factor

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

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

Rewrite using trig identities

= cos^{2} (x) \cdot 2

= 2 cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{tan ( x )} + tan (x) = sec (x) \cdot csc (x)

cos (\frac{3 π}{2} + x) = sin (x)

csc (2 A) + cot (2 A) = cot (A)

1 - sin (θ) = cos (θ)

csc^{2} (x) = cot^{2} (x) + 1