Is sin(θ)cos(θ)csc^2(θ)=cot(θ) ?

The answer to whether sin(θ)cos(θ)csc^2(θ)=cot(θ) is True

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prove sin(θ)cos(θ)csc^2(θ)=cot(θ)

prove

sin (θ) cos (θ) csc^{2} (θ) = cot (θ)

True

Solution steps

sin (θ) cos (θ) csc^{2} (θ) = cot (θ)

Manipulating left side

sin (θ) cos (θ) csc^{2} (θ)

Express with sin, cos

= \frac{cos ( θ )}{sin ( θ )}

Use the basic trigonometric identity:

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

= cot (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{cos ( x ) sec ( x )}{cot ( x )} = tan (x)

8 cos^{4} (θ - 8) sin^{4} (θ) = 8 cos (2 θ)

csc (θ) sec (θ) - csc (θ) cos (θ) = tan (θ)

\frac{1 - cos ( 2 θ ) + sin ( 2 θ )}{1 + cos ( 2 θ ) + sin ( 2 θ )} = tan (θ)

Is sin(θ)cos(θ)csc^2(θ)=cot(θ) ?
The answer to whether sin(θ)cos(θ)csc^2(θ)=cot(θ) is True