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

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

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

prove

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

True

Solution steps

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

Manipulating right side

cos^{2} (x)

Rewrite using trig identities

cos^{2} (x)

Use the Double Angle identity:

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

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

csc (x) tan (x) = sec (x)

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

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

cot (x) sec (x) sin (x) = 1

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