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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

= \frac{1 - cos ^{2} ( x )}{cos ^{2} ( x )}

Rewrite using trig identities

= \frac{sin ^{2} ( x )}{cos ^{2} ( x )}

Rewrite using trig identities

tan^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{csc ^{2} ( x )} + cos^{2} (x) = 1

2 cos^{2} (θ) - 1 = 1 - 2 sin^{2} (θ)

cot (x) = \frac{csc ( x )}{sec ( x )}

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

tan (a) = \frac{sin ( a )}{cos ( a )}

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