Is (cos^2(t))/(sin(t))=csc(t)-sin(t) ?

The answer to whether (cos^2(t))/(sin(t))=csc(t)-sin(t) is True

Popular >

prove (cos^2(t))/(sin(t))=csc(t)-sin(t)

prove

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

True

Solution steps

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

Manipulating right side

csc (t) - sin (t)

Express with sin, cos

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

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

sec (u) + tan (u) = \frac{cos ( u )}{1 - sin ( u )}

cos (x - \frac{π}{6}) - cos (x + \frac{π}{6}) = sin (x)

cos (\frac{3 π}{2} + θ) = sin (θ)

csc^{2} (θ) - cos^{2} (θ) csc^{2} (θ) = 1

Is (cos^2(t))/(sin(t))=csc(t)-sin(t) ?
The answer to whether (cos^2(t))/(sin(t))=csc(t)-sin(t) is True