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

prove sin(t)csc(t)=1

Solution

prove

sin (t) csc (t) = 1

True

Solution steps

sin (t) csc (t) = 1

Manipulating left side

sin (t) csc (t)

csc (t) sin (t) = 1

csc (t) sin (t)

Express with sin, cos

csc (t) sin (t)

Use the basic trigonometric identity:

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

= \frac{1}{sin ( t )} sin (t)

\frac{1}{sin ( t )} sin (t) = 1

\frac{1}{sin ( t )} sin (t)

Multiply fractions:

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

= \frac{1 sin ( t )}{sin ( t )}

Cancel the common factor:

sin (t)

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

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

p ro v e sec (2 θ) = \frac{sec ^{2} ( θ )}{2 - sec ^{2} ( θ )}

p ro v e tan (x) + cot (x) = \frac{2}{sin ( 2 x )}

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

p ro v e \frac{sin ( 2 x )}{sin ( x )} - \frac{cos ( 2 x )}{cos ( x )} = sec (x)