Is (sin(x))/(csc(x))=sin^2(x) ?

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

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prove (sin(x))/(csc(x))=sin^2(x)

prove

\frac{sin ( x )}{csc ( x )} = sin^{2} (x)

True

Solution steps

\frac{sin ( x )}{csc ( x )} = sin^{2} (x)

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

= \frac{sin ( x )}{\frac{1}{s i n ( x )}}

Simplify

\frac{sin ( x )}{\frac{1}{s i n ( x )}} : sin^{2} (x)

\frac{sin ( x )}{\frac{1}{s i n ( x )}}

Apply the fraction rule:

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

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

Apply rule

\frac{a}{1} = a

= sin (x) sin (x)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

sin (x) sin (x) = sin^{1 + 1} (x)

= sin^{1 + 1} (x)

Add the numbers:

1 + 1 = 2

= sin^{2} (x)

= sin^{2} (x)

= sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

tan (2 A) - tan (A) = tan (A) sec (2 A)

\frac{1}{1 - csc ( x )} - \frac{1}{1 + csc ( x )} = - 2 tan (x) sec (x)

- 2 sin (x - y) sin (x + y) = cos (2 x) - cos (2 y)

\frac{csc ^{2} ( x )}{cot ( x )} = csc (x) \cdot sec (x)

(1 - sin (x)) + (1 + sin (x)) = 2 cos (x)

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