Is sec^4(θ)-tan^4(θ)=2tan^2(θ)+1 ?

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

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prove sec^4(θ)-tan^4(θ)=2tan^2(θ)+1

prove

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

True

Solution steps

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

Manipulating left side

sec^{4} (θ) - tan^{4} (θ)

Factor

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

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

Rewrite using trig identities

= 2 tan^{2} (θ) + 1

We showed that the two sides could take the same form

\Rightarrow True

tan^{2} (x) (1 + cot^{2} (x)) = sec^{2} (x)

\frac{1 - sin ( x )}{cos ( x )} = 1 - tan (x)

1 - cos^{2} (x) - cos^{2} (x) = 1 - 2 cos^{2} (x)

\frac{( 1 + cot ^{2} ( x ) )}{sec ^{2} ( x )} = cot^{2} (x)

cot (s) + tan (s) = sec (s) csc (s)

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