Is sec(x)+tan(x)= 1/((sec(x)-tan(x))) ?

The answer to whether sec(x)+tan(x)= 1/((sec(x)-tan(x))) is True

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prove sec(x)+tan(x)= 1/((sec(x)-tan(x)))

prove

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

True

Solution steps

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

Manipulating right side

\frac{1}{sec ( x ) - tan ( x )}

Rewrite using trig identities

= sec (x) + tan (x)

We showed that the two sides could take the same form

\Rightarrow True

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

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

2 (sec (x) cot (x)) = 2 csc (x)

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

cos (a) cot (a) = csc (a) - sin (a)

Is sec(x)+tan(x)= 1/((sec(x)-tan(x))) ?
The answer to whether sec(x)+tan(x)= 1/((sec(x)-tan(x))) is True