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

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

Popular >

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

prove

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

True

Solution steps

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

Manipulating left side

sin (x) - csc (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

tan (θ) cot (θ) = cos^{2} (θ) + sin^{2} (θ)

cos (θ) = sin (3 θ + 62)

sin (π \cdot x) + sin (π \cdot (10 - x)) = 0

cot (2 θ) = \frac{1}{2} (tan (θ) - cot (θ))

sin (4 x) = (2) (sin (2 x)) (cos (2 x))

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