Is csc^4(x)-cot^4(x)=2csc^2(x)+1 ?

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

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prove csc^4(x)-cot^4(x)=2csc^2(x)+1

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

csc^{4} (1) - cot^{4} (1) = 1.82456 \dots

csc^{4} (1) - cot^{4} (1)

Refine to a decimal form

= 1.82456 \dots

2 csc^{2} (1) + 1 = 3.82456 \dots

2 csc^{2} (1) + 1

Refine to a decimal form

= 3.82456 \dots

The two sides are not equal

\Rightarrow False

(1 - cos (x)) (1 + sec (x)) = sin (x) cos (x)

2 sin^{2} (x) = 1

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

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

cos (3 x) = 4 (cos^{3} (x)) - 3 cos (x)

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