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

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

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

prove

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

True

Solution steps

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

Manipulating left side

tan^{2} (x)

Use the Pythagorean identity:

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

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

= sec^{2} (x) - 1

Factor

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

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

We showed that the two sides could take the same form

\Rightarrow True

cot (θ) sin (θ) = csc (θ)

\frac{sin ( 2 x ) + sin ( 4 x )}{cos ( 2 x ) + cos ( 4 x )} = tan (3 x)

sec (A) csc (A) = cos (A) tan (A)

\frac{1}{tan ( b )} + tan (b) = \frac{sec ^{2} ( b )}{tan ( b )}

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

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