Is 1/(1-sin(x))+1/(1+sin(x))=2sec(x) ?

The answer to whether 1/(1-sin(x))+1/(1+sin(x))=2sec(x) is False

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prove 1/(1-sin(x))+1/(1+sin(x))=2sec(x)

prove

\frac{1}{1 - sin ( x )} + \frac{1}{1 + sin ( x )} = 2 sec (x)

False

Solution steps

\frac{1}{1 - sin ( x )} + \frac{1}{1 + sin ( x )} = 2 sec (x)

Show that the two sides are not equal

For

\frac{1}{1 - sin ( x )} + \frac{1}{1 + sin ( x )} = 2 sec (x)

plug in

x = 1

\frac{1}{1 - sin ( 1 )} + \frac{1}{1 + sin ( 1 )} = 6.85103 \dots

\frac{1}{1 - sin ( 1 )} + \frac{1}{1 + sin ( 1 )}

Refine to a decimal form

= 6.85103 \dots

2 sec (1) = 3.70163 \dots

2 sec (1)

Refine to a decimal form

= 3.70163 \dots

The two sides are not equal

\Rightarrow False

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

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

(6 cos^{2} (x) - 6 sin^{2} (x)) = 6 - 12 sin^{2} (x)

1 + \frac{1}{tan ^{2} ( x )} = csc^{2} (x)

Is 1/(1-sin(x))+1/(1+sin(x))=2sec(x) ?
The answer to whether 1/(1-sin(x))+1/(1+sin(x))=2sec(x) is False