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

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

\frac{1 + tan ( θ )}{cos ( θ ) + sin ( θ )} = sec (θ)

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