Is sin((3pi)/2+θ)=-cos(θ) ?

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

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prove sin((3pi)/2+θ)=-cos(θ)

prove

sin (\frac{3 π}{2} + θ) = - cos (θ)

True

Solution steps

sin (\frac{3 π}{2} + θ) = - cos (θ)

Manipulating left side

sin (\frac{3 π}{2} + θ)

Rewrite using trig identities

= - cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

2 cot (2 x) = cot (x) - tan (x)

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

\frac{sec ( x )}{cot ( x ) + tan ( x )} = sin (x)

cos (\frac{π}{2} + x) = - sin (x)

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