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

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

p ro v e 2 \cdot cos (x) \cdot sin (x) = sin (2 x)

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

p ro v e \frac{1 + sec ( θ )}{sec ^{2} ( θ )} = 1 + cos^{2} (θ)

p ro v e \frac{1}{csc ( x ) + 1} + \frac{1}{csc ( x ) - 1} = 2 sec (x) tan (x)

p ro v e 25 cos^{2} (x) = 25 - 25 sin^{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