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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Add similar elements:

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

= 2 sin^{2} (x)

= 2 sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

cos (x) + sin (x) = 1

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

sin^{2} (u) (cot^{2} (u) + 1) = 1

\frac{1 + csc ( x )}{cos ( x ) + cot ( x )} = sec (x)

cos (x + \frac{π}{6}) = - sin (x - \frac{π}{3})

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