Is (1+tan^2(θ))/(1-tan^2(θ))=sec(2θ) ?

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

Popular >

prove (1+tan^2(θ))/(1-tan^2(θ))=sec(2θ)

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

= \frac{cos ^{2} ( θ ) + sin ^{2} ( θ )}{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} (3 x) - sin^{2} (3 x) = cos (6 x)

sec^{2} (Θ) csc^{2} (Θ) = sec^{2} (Θ) + csc^{2} (Θ)

\frac{cos ( t )}{1 - sin ( t )} = sec (t) + tan (t)

(sec (x) - 1)^{4} = 2 tan^{2} (x) - tan^{4} (x)

sin (2 x) = 2 \frac{cos ( x )}{csc ( x )}

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