Is tan^4(θ)-sec^4(θ)=1-2sec^2(θ) ?

The answer to whether tan^4(θ)-sec^4(θ)=1-2sec^2(θ) is True

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prove tan^4(θ)-sec^4(θ)=1-2sec^2(θ)

prove

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

True

Solution steps

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

Manipulating left side

tan^{4} (θ) - sec^{4} (θ)

Factor

- sec^{4} (θ) + tan^{4} (θ) : (tan^{2} (θ) + sec^{2} (θ)) (tan (θ) + sec (θ)) (tan (θ) - sec (θ))

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

Rewrite using trig identities

= 1 - 2 sec^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

sec (x) - tan (x) = cos (x)

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

\frac{cos ^{2} ( t )}{cot ( t )} = cos (t) sin (t)

4 sec^{2} (θ) - 3 = 1 + 4 tan^{2} (θ)

Is tan^4(θ)-sec^4(θ)=1-2sec^2(θ) ?
The answer to whether tan^4(θ)-sec^4(θ)=1-2sec^2(θ) is True