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

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

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

prove

cos (\frac{3 π}{2} - x) = - sin (x)

True

Solution steps

cos (\frac{3 π}{2} - x) = - sin (x)

Manipulating left side

cos (\frac{3 π}{2} - x)

Rewrite using trig identities

= - sin (x)

We showed that the two sides could take the same form

\Rightarrow True

sin (π + θ) = - sin (θ)

\frac{tan ( x ) cot ( x )}{sin ( x )} = csc (x)

csc^{2} (x) \cdot tan^{2} (x) - 1 = tan^{2} (x)

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

cos^{2} (x) = \frac{( 1 + cos ( 2 x ) )}{2}

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