Is (sec(x)-1)(sec(x)+1)=tan^2(x) ?

The answer to whether (sec(x)-1)(sec(x)+1)=tan^2(x) is True

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prove (sec(x)-1)(sec(x)+1)=tan^2(x)

prove

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

True

Solution steps

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

Manipulating left side

(sec (x) - 1) (sec (x) + 1)

Expand

(sec (x) + 1) (sec (x) - 1) : sec^{2} (x) - 1

= sec^{2} (x) - 1

Use the Pythagorean identity:

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

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

= tan^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

(csc (θ) + cot (θ)) (csc (θ) - cot (θ)) = 1

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

\frac{sin ( 2 x )}{sin ( x )} = 2 cos (x)

tan^{3} (x) = tan (x) sec^{2} (x) - tan (x)

Is (sec(x)-1)(sec(x)+1)=tan^2(x) ?
The answer to whether (sec(x)-1)(sec(x)+1)=tan^2(x) is True