Is cos(y)csc(y)=cot(y) ?

The answer to whether cos(y)csc(y)=cot(y) is True

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prove cos(y)csc(y)=cot(y)

prove

cos (y) csc (y) = cot (y)

True

Solution steps

cos (y) csc (y) = cot (y)

Manipulating left side

cos (y) csc (y)

Express with sin, cos

csc (y) cos (y)

Use the basic trigonometric identity:

csc (y) = \frac{1}{sin ( y )}

= \frac{1}{sin ( y )} cos (y)

Simplify

\frac{1}{sin ( y )} cos (y) : \frac{cos ( y )}{sin ( y )}

\frac{1}{sin ( y )} cos (y)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 cos ( y )}{sin ( y )}

Multiply:

1 \cdot cos (y) = cos (y)

= \frac{cos ( y )}{sin ( y )}

= \frac{cos ( y )}{sin ( y )}

= \frac{cos ( y )}{sin ( y )}

Use the basic trigonometric identity:

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

= cot (y)

We showed that the two sides could take the same form

\Rightarrow True

\frac{tan ( a )}{sin ( a )} - sec (a) = 0

\frac{1}{cot ( θ )} = \frac{tan ( θ )}{sin ( θ )}

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

2 cos (θ) = \frac{2}{sec ( θ )}

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