Is 1-tan^4(θ)=2sec^2(θ)-sec^4(θ) ?

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

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prove 1-tan^4(θ)=2sec^2(θ)-sec^4(θ)

prove

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

True

Solution steps

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

Manipulating right side

2 sec^{2} (θ) - sec^{4} (θ)

Factor

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

= (2 - sec^{2} (θ)) sec^{2} (θ)

Rewrite using trig identities

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

Expand

(1 + tan^{2} (θ)) (1 - tan^{2} (θ)) : 1 - tan^{4} (θ)

= 1 - tan^{4} (θ)

We showed that the two sides could take the same form

\Rightarrow True

(sec (x) + tan (x)) (csc (x) - 1) = cot (x)

cos (\frac{π}{2}) + 1 = sin (\frac{π}{2})

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

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

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

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