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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Rewrite using trig identities

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

Use the Pythagorean identity:

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 - sin ( a )}{1 + sin ( a )} = \frac{cos ( a )}{1 + sin ( a )}

2 \cdot cos (x) \cdot sin (x) = sin (2 x)

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

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

2 cos^{2} (x) = cos (2 x)

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