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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 - tan ^{4} ( x )}{sec ^{2} ( x )} = 1 - tan^{2} (x)

tan^{2} (x) = sec (x) csc (x) tan (x) - 1

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

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

3 - sec^{2} (x) = 2 - tan^{2} (x)

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