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

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

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

prove

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

True

Solution steps

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

Manipulating left side

2 cos^{2} (x) - 1

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

sin (x) = - 1 = sin (0) = - 1

sin (\frac{3 π}{2} - θ) = cos (θ)

sin (2 x) = 2 (cos (x)) (cos (\frac{π}{2} - x))

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

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

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