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

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

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prove 1/(sec^2(x))=sin^2(x)+cos(2x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1}{sec ^{2} ( x )}

Express with sin, cos

= cos^{2} (x)

Rewrite using trig identities

= 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

csc (2 y) = csc (y) 7

csc^{2} (θ) (1 - cos^{2} (θ)) = cos (\frac{π}{2})

tan (x) + cot (2 x) = sec (2 x)

csc (θ) (csc (θ) - sin (θ)) = cot^{2} (θ)

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

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