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

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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

\frac{sin ( a + b )}{sin ( a - b )} = \frac{1 + cot ( a ) tan ( b )}{1 - cot ( a ) tan ( b )}

cot (x + π) = cot (x)

(cos (x) + tan (x))^{2} = csc^{2} (x) sec^{2} (x)

tan (x) (2 - cos (x))^{2} = 0

2 cos (a) - sin (2 a) csc (a) = 0

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