Is sec(2θ)=(sec^2(θ))/(1-tan^2(θ)) ?

The answer to whether sec(2θ)=(sec^2(θ))/(1-tan^2(θ)) is True

Popular >

prove sec(2θ)=(sec^2(θ))/(1-tan^2(θ))

prove

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

True

Solution steps

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

Manipulating right side

\frac{sec ^{2} ( θ )}{1 - tan ^{2} ( θ )}

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{cos ( 2 θ )}

Rewrite using trig identities

sec (2 θ)

We showed that the two sides could take the same form

\Rightarrow True

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

tan (θ) + cot (θ) = sec (θ) \cdot csc (θ)

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

\frac{cos ( x ) csc ( x )}{cot ^{2} ( x )} = tan (x)

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

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