Is (cos(2x))/(sin(x))=cos(x)cot(x)-sin(x) ?

The answer to whether (cos(2x))/(sin(x))=cos(x)cot(x)-sin(x) is True

Popular >

prove (cos(2x))/(sin(x))=cos(x)cot(x)-sin(x)

prove

\frac{cos ( 2 x )}{sin ( x )} = cos (x) cot (x) - sin (x)

True

Solution steps

\frac{cos ( 2 x )}{sin ( x )} = cos (x) cot (x) - sin (x)

Manipulating left side

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

Rewrite using trig identities

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

Manipulating right side

cos (x) cot (x) - sin (x)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

cot^{2} (2 x) + cos^{2} (2 x) + sin^{2} (2 x) = csc^{2} (2 x)

sin^{2} (x) - 4 cos^{2} (x) = 1 - 5 cos^{2} (x)

25 sec^{2} (5 x) = 25 + (5 tan (5 x))^{2}

tan (x) = csc (2 x) - cot (2 x)

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

Is (cos(2x))/(sin(x))=cos(x)cot(x)-sin(x) ?
The answer to whether (cos(2x))/(sin(x))=cos(x)cot(x)-sin(x) is True