Is sin(2x)csc(2x)=1 ?

The answer to whether sin(2x)csc(2x)=1 is True

prove sin(2x)csc(2x)=1

prove

sin (2 x) csc (2 x) = 1

True

Solution steps

sin (2 x) csc (2 x) = 1

Manipulating left side

sin (2 x) csc (2 x)

Express with sin, cos

csc (2 x) sin (2 x)

Use the basic trigonometric identity:

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

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

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

\frac{1}{sin ( 2 x )} sin (2 x)

Multiply fractions:

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

= \frac{1 \cdot sin ( 2 x )}{sin ( 2 x )}

Cancel the common factor:

sin (2 x)

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

p ro v e \frac{cot ^{2} ( x ) - 1}{csc ( x ) + 1} = csc (x) - 1

p ro v e \frac{( cos ( π + x ) )}{cos ( \frac{3 π}{2} - x )} = cot (x)

p ro v e sin (12 0^{\circ}) = sin (18 0^{\circ} - 6 0^{\circ})

p ro v e \frac{sin ( 2 x )}{tan ( 2 x )} = 1 - 2 sin^{2} (x)

p ro v e cot (a) = tan (\frac{π}{2} - a)