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

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

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

prove

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

True

Solution steps

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

Manipulating left side

1 + cos^{2} (x)

Rewrite using trig identities

1 + cos^{2} (x)

Use the Pythagorean identity:

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

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

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

Simplify

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

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

= 2 - sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (\frac{3 π}{2} + 0) = - cos (0)

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

\frac{tan ( θ ) cot ( θ )}{cos ( θ )} = sec (θ)

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

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