Is sec^2(θ)-2tan(θ)=(tan(θ)-1)^2 ?

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

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prove sec^2(θ)-2tan(θ)=(tan(θ)-1)^2

prove

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

True

Solution steps

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

Manipulating right side

(tan (θ) - 1)^{2}

Expand

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

= 1 + tan^{2} (θ) - 2 tan (θ)

Rewrite using trig identities

= - 2 tan (θ) + sec^{2} (θ)

= sec^{2} (θ) - 2 tan (θ)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{csc ( x )} + 1 = sin (x) + 1

25 sin^{2} (x) + 25 cos^{2} (x) = 25

cot (x) sin (x) sec (x) = 1

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

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

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