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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

Simplify

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

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

Group like terms

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

Add similar elements:

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

2 cos^{3} (x) - cos (x) = \frac{cos ^{2} ( x ) - sin ^{2} ( x )}{sec ( x )}

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

\frac{cos ( 5 x ) - cos ( 3 x )}{sin ( 5 x ) + sin ( 3 x )} = - tan (x)

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

\frac{1}{tan ( x )} = cot (x)

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