Is sec((3pi)/2-x)=-csc(x) ?

The answer to whether sec((3pi)/2-x)=-csc(x) is True

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prove sec((3pi)/2-x)=-csc(x)

prove

sec (\frac{3 π}{2} - x) = - csc (x)

True

Solution steps

sec (\frac{3 π}{2} - x) = - csc (x)

Manipulating left side

sec (\frac{3 π}{2} - x)

Rewrite using trig identities

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

Rewrite using trig identities

- csc (x)

We showed that the two sides could take the same form

\Rightarrow True

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

cos (x) + sin (x) tan (x) = \frac{1}{cos ( x )}

cos (α + β) - cos (α - β) = - 2 sin (α) sin (β)

tan (θ) \cdot csc (θ) = \frac{1}{cos ( θ )}

cos (2 θ) = \frac{csc ^{2} ( θ ) - 2}{csc ^{2} ( θ )}

Is sec((3pi)/2-x)=-csc(x) ?
The answer to whether sec((3pi)/2-x)=-csc(x) is True