Which expression is equivalent to tangent of open paren theta over 2 close paren times open paren negative sine theta close paren ?

Use the identity tan(θ/2) = sin θ/(1 + cos θ). Then tan(θ/2)(−sin θ) = −sin² θ/(1 + cos θ) = −(1 − cos θ) = −1 + cos θ, which is choice C.

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