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

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

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

prove

sin (\frac{3 π}{2} + x) = - cos (x)

True

Solution steps

sin (\frac{3 π}{2} + x) = - cos (x)

Manipulating left side

sin (\frac{3 π}{2} + x)

Rewrite using trig identities

= - cos (x)

We showed that the two sides could take the same form

\Rightarrow True

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

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

sec (u) + tan (u) = \frac{cos ( u )}{1 - sin ( u )}

cos (x - \frac{π}{6}) - cos (x + \frac{π}{6}) = sin (x)

cos (\frac{3 π}{2} + θ) = sin (θ)

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