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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

Simplify

tan^{2} (x) + 1 + tan^{2} (x) : 2 tan^{2} (x) + 1

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

Group like terms

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

Add similar elements:

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

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

p ro v e cot (x + π) = cot (x)

p ro v e tan (x) (2 - cos (x))^{2} = 0

p ro v e 1 - 2 sin^{2} (x) = - 1 + 2 cos^{2} (x)

p ro v e \frac{1}{sin ( x ) cos ( x )} = 2 csc (2 x)

p ro v e 81 - 9 (3 sin (x))^{2} = 1

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