Is csc(θ)= 1/(sin(θ)) ?

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

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prove csc(θ)= 1/(sin(θ))

prove

csc (θ) = \frac{1}{sin ( θ )}

True

Solution steps

csc (θ) = \frac{1}{sin ( θ )}

Use the basic trigonometric identity:

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

\Rightarrow True

cos^{3} (x) + sin^{2} (x) cos (x) = cos (x)

cos^{2} (x) - cos^{4} (x) = cos^{2} (x) sin^{2} (x)

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

sin (θ) cos (θ) (tan (θ) + cot (θ)) = 1

tan (x) = \frac{sec ( x )}{csc ( x )}