Is csc(x)-sin(x)=cos(x)*cot(x) ?

The answer to whether csc(x)-sin(x)=cos(x)*cot(x) is True

Popular >

prove csc(x)-sin(x)=cos(x)*cot(x)

prove

csc (x) - sin (x) = cos (x) \cdot cot (x)

True

Solution steps

csc (x) - sin (x) = cos (x) cot (x)

Manipulating left side

csc (x) - sin (x)

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

cos (x) cot (x)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{sec ^{2} ( θ )}{tan ( θ )} = sec (θ) csc (θ)

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

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

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

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