Is cos(x-(3pi)/2)=-sin(x) ?

The answer to whether cos(x-(3pi)/2)=-sin(x) is True

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prove cos(x-(3pi)/2)=-sin(x)

prove

cos (x - \frac{3 π}{2}) = - sin (x)

True

Solution steps

cos (x - \frac{3 π}{2}) = - sin (x)

Manipulating left side

cos (x - \frac{3 π}{2})

Rewrite using trig identities

= - sin (x)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{cot ( x ) tan ( x )}{cos ( x )} = sec (x)

\frac{sin ( θ )}{cos ( θ )} = tan (θ)

cos (x) tan (x) csc (x) = 1

cos (θ) cot (θ) + sin^{2} (θ) csc (θ) = csc (θ)

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