sinθ + cosec θ = 2, then the value of sin 99 θ + cosec 99 θ is:
2
The correct answer is 2.
If $\sin \theta = -1$, then $\text{cosec } \theta = -1$, and $\sin \theta + \text{cosec } \theta = -1 + (-1) = -2$. This does not match the condition. Therefore, the only possibility is $\sin \theta = 1$, which leads to $\text{cosec } \theta = 1$. This confirms our previous finding obtained by solving the quadratic equation.
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