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If $\sin θ_{1} \sin θ_{2} - \cos θ_{1} \cos θ_{2} + 1 = 0$ then the value of $\tan (θ_{1} / 2) \cot (θ_{2} / 2)$ is equal to

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Correct option is A

sin⁡θ1sin⁡θ2−cos⁡θ1cos⁡θ2=−1 or cos⁡θ1+θ2=1⇒ θ1+θ2=2nπ,n∈1 or θ12+θ22=nπ Thus, tan⁡θ12cot⁡θ22=tan⁡θ12cot⁡nπ−θ12 =−tan⁡θ12cot⁡θ12=−1

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If sin⁡θ1sin⁡θ2−cos⁡θ1cos⁡θ2+1=0then the value of tan⁡θ1/2cot⁡θ2/2 is equal to

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If $\sin θ_{1} \sin θ_{2} - \cos θ_{1} \cos θ_{2} + 1 = 0$ then the value of $\tan (θ_{1} / 2) \cot (θ_{2} / 2)$ is equal to