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

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

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

prove

sin (x - \frac{3 π}{2}) = cos (x)

True

Solution steps

sin (x - \frac{3 π}{2}) = cos (x)

Manipulating left side

sin (x - \frac{3 π}{2})

Rewrite using trig identities

= cos (x)

We showed that the two sides could take the same form

\Rightarrow True

cos (x + 2 π) = cos (x)

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

\frac{cot ^{2} ( x )}{1 + csc ( x )} = csc (x) - 1

\frac{sin ^{2} ( θ )}{1 - cos ( θ )} = 1 + cos (θ)

csc (2 θ) = \frac{1}{2} sec (θ) csc (θ)