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

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

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

csc^{4} (x) - cot^{4} (x) = 2 sec^{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 sec^{2} (1) - 1 = 5.85103 \dots

2 sec^{2} (1) - 1

Refine to a decimal form

= 5.85103 \dots

The two sides are not equal

\Rightarrow False

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

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

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

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

tan (x) (cos (x) + cot (x)) = sin (x) + 1

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