Is (tan(x))(sin(x))=sec(x)-cos(x) ?

The answer to whether (tan(x))(sin(x))=sec(x)-cos(x) is True

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prove (tan(x))(sin(x))=sec(x)-cos(x)

prove

(tan (x)) (sin (x)) = sec (x) - cos (x)

True

Solution steps

tan (x) sin (x) = sec (x) - cos (x)

Manipulating left side

tan (x) sin (x)

Express with sin, cos

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

Rewrite using trig identities

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

Manipulating right side

sec (x) - cos (x)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

tan (α) + cot (α) = sec (α) csc (α)

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

cot (x) tan (x) = 1

cos^{2} (a) - sin^{2} (a) = 1 - 2 sin^{2} (a)

tan (u) cot (u) - sin^{2} (u) = cos^{2} (u)

Is (tan(x))(sin(x))=sec(x)-cos(x) ?
The answer to whether (tan(x))(sin(x))=sec(x)-cos(x) is True