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

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

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prove sec(2x)= 1/(1-2sin^2(x))

prove

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

True

Solution steps

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

Manipulating left side

sec (2 x)

Express with sin, cos

sec (2 x)

Use the basic trigonometric identity:

sec (x) = \frac{1}{cos ( x )}

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

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

Rewrite using trig identities

\frac{1}{cos ( 2 x )}

Use the Double Angle identity:

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

cos (3 θ) + cos (θ) = 4 cos^{3} (θ) - 2 cos (θ)

cos (a + b) = cos (a) cos (b) - sin (a) sin (b)

cos^{7} (x) = (1 - sin^{2} (x))^{3} cos (x)

(1 + tan (θ))^{2} = sec^{2} (θ) + 2 tan (θ)

\frac{1 + cot ^{2} ( x )}{2 cot ( x )} = csc (2 x)

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