Is 1+tan^2(x)=cos^2(x)+sin^2(x) ?

The answer to whether 1+tan^2(x)=cos^2(x)+sin^2(x) is False

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prove 1+tan^2(x)=cos^2(x)+sin^2(x)

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

1 + tan^{2} (1) = 3.42551 \dots

1 + tan^{2} (1)

Refine to a decimal form

= 3.42551 \dots

cos^{2} (1) + sin^{2} (1) = 1

cos^{2} (1) + sin^{2} (1)

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

= 1

= 1

The two sides are not equal

\Rightarrow False

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cos^{2} (2 t) + sin^{2} (2 t) = 1

tan (α) + cot (2 α) = sec (2 α)

tan (x + \frac{π}{3}) = \frac{tan ( x ) + 3}{1 - 3 tan ( x )}

Is 1+tan^2(x)=cos^2(x)+sin^2(x) ?
The answer to whether 1+tan^2(x)=cos^2(x)+sin^2(x) is False