Is csc^4(θ)-cot^4(θ)=2cot^2(θ)+1 ?

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

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prove csc^4(θ)-cot^4(θ)=2cot^2(θ)+1

prove

csc^{4} (θ) - cot^{4} (θ) = 2 cot^{2} (θ) + 1

True

Solution steps

csc^{4} (θ) - cot^{4} (θ) = 2 cot^{2} (θ) + 1

Manipulating left side

csc^{4} (θ) - cot^{4} (θ)

Factor

- cot^{4} (θ) + csc^{4} (θ) : (csc^{2} (θ) + cot^{2} (θ)) (csc (θ) + cot (θ)) (csc (θ) - cot (θ))

= (- cot (θ) + csc (θ)) (cot (θ) + csc (θ)) (cot^{2} (θ) + csc^{2} (θ))

Rewrite using trig identities

= 2 cot^{2} (θ) + 1

We showed that the two sides could take the same form

\Rightarrow True

sec (b) cot (b) = csc (b)

\frac{1 - cos ( 2 θ )}{sin ( 2 θ )} = tan (θ)

\frac{cos ( 3 x )}{sin ( x )} + \frac{sin ( 3 x )}{cos ( x )} = 2 cot (2 x)

sin (A + B) = sin (A) + sin (B)

\frac{cot ^{2} ( B ) - cos ^{2} ( B )}{csc ^{2} ( B ) - 1} = cos^{2} (B)

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