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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (2 x) = \frac{1 + cos ( 4 x )}{2}

sin^{2} (θ) csc^{2} (θ) - sin^{2} (θ) = cos^{2} (θ)

cos (x + \frac{π}{3}) + sin (x - \frac{π}{6}) = 0

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

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

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