Is cos(θ+(3pi)/2)=sin(θ) ?

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

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prove cos(θ+(3pi)/2)=sin(θ)

prove

cos (θ + \frac{3 π}{2}) = sin (θ)

True

Solution steps

cos (θ + \frac{3 π}{2}) = sin (θ)

Manipulating left side

cos (θ + \frac{3 π}{2})

Rewrite using trig identities

= sin (θ)

We showed that the two sides could take the same form

\Rightarrow True

cot (x) \cdot sec (x) \cdot sin (x) = 1

cot (θ) sin (θ) cos (θ) = 1 - sin^{2} (θ)

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

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

csc (θ) = \frac{1}{sin ( θ )}