Is sin^2(θ)+2cos^2(θ)-1=cos^2(θ) ?

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

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prove sin^2(θ)+2cos^2(θ)-1=cos^2(θ)

prove

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

True

Solution steps

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

Manipulating left side

sin^{2} (θ) + 2 cos^{2} (θ) - 1

Rewrite using trig identities

sin^{2} (θ) + 2 cos^{2} (θ) - 1

Use the Pythagorean identity:

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

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

= 2 cos^{2} (θ) - cos^{2} (θ)

Add similar elements:

2 cos^{2} (θ) - cos^{2} (θ) = cos^{2} (θ)

= cos^{2} (θ)

= cos^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{sin ( x ) cos ( x )} = 2 csc (2 x)

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

cos (θ) = - cos (- θ)

sin (θ) + cos (θ) = sin (θ + 4 5^{\circ})

\frac{sin ( 2 θ )}{sin ( θ )} = 2 cos (θ)

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