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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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