Is csc(θ)sin(θ)=-8/43 ?

The answer to whether csc(θ)sin(θ)=-8/43 is False

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prove csc(θ)sin(θ)=-8/43

prove

csc (θ) sin (θ) = - \frac{8}{43}

False

Solution steps

csc (θ) sin (θ) = - \frac{8}{43}

Show that the two sides are not equal

For

csc (θ) sin (θ) = - \frac{8}{43}

plug in

θ = 1

csc (1) sin (1) = 1

csc (1) sin (1)

Rewrite using trig identities:

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

sin (1)

Use the basic trigonometric identity:

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

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

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

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

csc (1) \frac{1}{csc ( 1 )}

Multiply fractions:

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

= \frac{1 \cdot csc ( 1 )}{csc ( 1 )}

Cancel the common factor:

csc (1)

= 1

= 1

The two sides are not equal

\Rightarrow False

csc (θ) sin (θ) - sin^{2} (θ) = cos^{2} (θ)

sin (\frac{π}{2} + x) = - cos (x)

tan^{2} (x) - sec (x) = 1

2 sin (π) = 5 sin (π)

tan (x) - \frac{1}{tan ( x )} = 2 sin^{2} (x) - 1