Is sec^2(x)-tan^2(x)=tan(x)cot(x) ?

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

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prove sec^2(x)-tan^2(x)=tan(x)cot(x)

prove

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

True

Solution steps

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

Manipulating right side

tan (x) cot (x)

Express with sin, cos

= 1

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{tan ( θ )}{tan ( θ ) - 1} = \frac{1}{1 - cot ( θ )}

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

2 cos (x) tan (x) csc (x) = 2

sec^{2} (y) - cot^{2} (\frac{π}{2} - y) = 1

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

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