Is (sin(x))/(cot(x))=sec(x)-cos(x) ?

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

Popular >

prove (sin(x))/(cot(x))=sec(x)-cos(x)

prove

\frac{sin ( x )}{cot ( x )} = sec (x) - cos (x)

True

Solution steps

\frac{sin ( x )}{cot ( x )} = sec (x) - cos (x)

Manipulating left side

\frac{sin ( x )}{cot ( 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

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

cos (3 θ) + cos (θ) = 4 cos^{3} (θ) - 2 cos (θ)

cos (a + b) = cos (a) cos (b) - sin (a) sin (b)

cos^{7} (x) = (1 - sin^{2} (x))^{3} cos (x)

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

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