Is 1+cos^2(θ)=2cos^2(θ)+sin^2(θ) ?

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

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prove 1+cos^2(θ)=2cos^2(θ)+sin^2(θ)

prove

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

True

Solution steps

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

Manipulating right side

2 cos^{2} (θ) + sin^{2} (θ)

Rewrite using trig identities

= cos^{2} (θ) + 1

= 1 + cos^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

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

\frac{1 - sin ( x )}{1 - csc ( x )} = - sin (x)

1 + cos (10 y) = 2 cos^{2} (5 y)

cos (a) tan (a) = sin (a)

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